I've been reading the manga for a while before the anime adaptation came out, and it has even more moments of that style of humour with Nagate Tanikaze being injured in various ways. And no, I'm pretty sure that humour isn't unintentional. The manga features it so often that it seems to be a purposeful theme.
I'm not sure why you're specifically comparing it to Attack on Titan since it's not so much breaching the wall as aliens attacking the ship, which is fairly standard in sci-fi shows in general. I would say that the feel of it isn't the same as AoT either since the main character (Tanikaze) isn't anything like the angry/angsty Eren from AoT.
As for some of the other things you've mentioned that I get the sense you're sort of mocking, I don't really agree, but some of this may be because the manga sometimes explains things a bit better than the show can. I'll detail each below.
Their ship being partly a "rock", as you put it, is because it both serves the function of continuous mining of the asteroid's resources and for protection since it's naturally pretty thick and obviously doesn't need to be built like how an artificial structure would be. However, I admit that one flaw to this idea might be that the thrusters would have a harder time accelerating such a ship/colony because of the sheer mass of the asteroid.
The whole Tanikaze not wanting to get caught and recycled part revolves around a somewhat gruesome system they have in place where the elderly at a certain point in life seem to be shuffled off to the organic recyclers, reactors, or something like that (I forget the exact word offhand). From my understanding, they've put this in place due to extreme stresses they've faced in the past and continuing on into the present. Certain resources are scarce, so they've basically enacted some severe population controls, both for explosive growth of the population originally after a massive loss of life during a past event and to avoid running out of resources in the present if the growth becomes too great. As I said, the concept certainly sounds awful and unethical, but there are plenty of sci-fi series out there that attempt to tackle some shocking societal possibilities.
There's also a major backstory as to why Tanikaze was down in the bowels of the ship away from others and the ruling structure, but that may not have been properly covered in the anime's first season (a second has been confirmed to be coming) because it only follows the first five and a half volumes of the manga. You definitely won't really understand that from the first three episodes, so don't judge that just yet at any rate. I won't explain exactly what the past story is right now to avoid spoilers, but I felt that it is a fairly understandable reason.
As to Lala Hiyama, the human-bear hybrid... Okay, I'll give you that one. It's on the weirder side of this series. I think part of her appearance is supposed to fit in with that odd sense of humour that the artist has; he often depicts himself as an insect in his short comics about his own life at the back of the books.
Regarding Izana Shinatose and the whole third gender thing, it was initially an interesting idea, but I admit that it could have been fleshed out better. Judging from what I've read of the manga so far (the first 10 volumes), it does sound like it works as you've described it: Shinatose's sex slowly starts to change according to who they are attracted to. How that works on a biological level exactly, I don't know. Unfortunately, the series so far hasn't really explained. I believe it was one of the last two volumes I'd read in which Shinatose has finally gone through some physical changes, but there weren't any details as to whether this occurs as an automatic process or if outside medical intervention is required to initiate a change to one of other two sexes. And yes, based on everything I've read, I've felt a little disappointment in that it could have raised more interesting questions about gender and sex but instead involves a fair amount of heteronormativity, traditional gender roles, etc.
I found the human photosynthesis part to be a unique concept, though. Again, like some of the stuff above, the manga later on details why this genetic change was put in place due to major problems in the past. I won't go into the specifics to avoid spoilers, but it's tied to the scarce resources that I mentioned earlier. People eating less could definitely ease that issue. However, if some of what makes it seem corny to you is the fairly abundant usage of girls and women sun-bathing as a form of fanservice, then I'm kind of with you on that. Despite that, I'm still intrigued by the idea. Whether this might actually be possible with genetic engineering by an advanced society... I don't know.
I'm not sure what you meant exactly by the Earth-like atmosphere and radiation parts. It seems rather obvious with a society living in space that they'd have breathable air inside the ship, and they could certainly find technological ways to block out forms of radiation that are from the harmful parts of the electromagnetic spectrum while letting through a certain amount of sunlight for people to photosynthesize with or just for lighting.
As for the ocean, it's again one of the series' wilder ideas, but it's perhaps not impossible considering how enormous their ship is and the fact that it's supposed to be a multi-generational colony. The ocean is displayed in the manga in relation to the main characters as a form of recreation, for viewing, etc., but I'm sure they'd have more practical uses for it too as a renewable source of food and perhaps some degree of atmospheric recycling if the ocean has a significant amount of algae in it. As with much of the above, there's some major backstory here as to why they'd have to build the ship as their long-term home similar to the Earth or any other habitable planet because they basically have nowhere else to go right now. Explaining would again involve spoilers.
I found the pacing to be generally okay considering it's supposed to be a sci-fi action series with moments of suspense, but this interpretation will vary from person to person of course. Regarding the photosynthesis lecture, I'm trying to recall which part that is. The one I'm thinking of right now isn't as you describe it, but it might be further along than where you are. The one I'm thinking of has a scientist (specifically not naming this character to avoid spoilers) in the past explaining why introducing human photosynthesis is necessary, and it actually makes some sense. If what you're referring to is in fact an earlier class lecture with Tanikaze in it, they may have covered the topic because Tanikaze is in the dark about this information and plenty of other things due to his growing up away from society. I vaguely recall no one else in the class being surprised at such things being mentioned in class probably precisely because they are already long used to these things. Tanikaze being out of the loop on this stuff kind of reinforces the above mentioned humour and the perception of him being an outsider trying to fit in.
Some of the information dump may seem worse in the anime adaptation because I do recall thinking that some informational stuff wasn't covered quite as well in the anime as I was watching it and comparing to what I'd read beforehand.
I don't think a high death toll is necessarily an indication of a series being bad either. If anything, it's a little unconventionally realistic. People die in wars, and the enemy they're facing is particularly difficult to the point that they're barely avoiding annihilation. Some of the dead characters aren't main characters, but that often happens in shows ("red shirts" dying essentially). That might explain why you can't remember some of these characters' names.
As for the Gauna (the alien race they're fighting), yes, some of the concepts involved have certainly been done before, like having cores that have to be penetrated to and then destroyed in specific ways or alien races that have a habit of making quick adaptations, and creatures with tentacles or tendrils are certainly nothing new in several different genres, including sci-fi. I didn't personally find this to ruin the fun of the series even if it's not entirely original, though.
Anyways, as a whole, I've enjoyed both the manga and the anime adaptation, so I'm a bit saddened that you don't care for it so far. I will say that with where I currently am in the manga, I've found that it seems to have worn some things a little thin and feels to me that it may have slid downwards a bit in terms of the excitement, interesting new concepts, mystery, and suspense from where it was at with that climactic Gauna-asteroid mission which they fittingly used for the anime's final arc. However, all of that is beyond what the first 12 episodes of the anime covers and doesn't reflect it as such. I'm hoping that maybe a little more of the series will make sense to you once you've finished all of the episodes.
I should also note that the CGI bugged me a bit, particularly with characters' faces sometimes. It works pretty well for the outer space stuff with the mecha, ship, and virtually anything non-human (and/or non-bear ^^; ). I know they went with the CGI to save on costs, though, and I'm fine with that rather than no adaptation at all.
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