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Before trying fouettes, I would definitely focus on getting close-to-perfect pirouettes. Learn how not to fall out of one, focus up the whole way while spotting. If you look down or fidget, then you won't be able to do many turns. And the obvious, stomach and butt are sucked in. As for pointe, you'll get used to it. It's actually easier to do many turns with a pointe shoe than flats. But a pointe shoe is elevated, so losing balance happens a lot. Fouttes, only thing I can tell you is to keep turning/spotting and lifting the leg when you whip it out.

before fouettes i'd try to get really good consistent doubles on both sides.
if your left side is bad, then you need turn on that side more to become more comfortable with it.

make sure that when you prep for a turn (from fourth, en dehor) your weight should be on the front leg (if turning from fifth it should be equally distributed), so much that you can lift you back leg off of the floor easily. make sure that your hips and torso are aligned and straight forward, not twisted, and make sure that your hips are flat. keep your lower abs (your core) really tight (keep breathing though). keep that feeling (stay relaxed and don't freak out/panick, it's just a turn) and exhale as you go into your plie, push off with both feet, inhale as you rise, immediately turning out from the hips as soon as your back foot leaves the floor. then keep everything nice and tight, and spot your head in the mirror if you have a mirror.
keep thinking about your lifting and opposition. to go up, you must push down. to keep myself stable in a turn i have to feel like my head and the back of my ears are being lifted by a string, feeling this all through my torso. from my waist and below i am thinking about drilling my toes into the floor. like something is pulling my head up, and my feet down. visuals can really help improve everything.

when you think you are finished with a turn make sure to really suck in and pull up for an extra lift and stop in the retire/passe and hold it before you close.

try even doing a single well controlled turn and stop in the passe (still in releve) and lift everything up, and your passe up higher, then close to fifth sous sus and plie deeply for finish. practice this on both sides and i promise every turn you do will improve.

key thing is to maintain your control and posture and don't panic. panic will send your body into distorted positions that are hard to turn from and then you will just be fighting yourself.

and when you do get to those fouettes treat them like a grande rond de jambe to second. start with a double pirrouette into the fouette to help with momentum. let the swing of your leg from the front to the second turn you, and then whip you foot straight into passe (no ronds en lair, or as my teacher calls it blender feet). remember to plie deeply in fouettes, it's very important in fouettes, so that you can spring back up to do another turn.
another tip: don't keep the weight in the heel of your feet. if you keep the weight in your plie in the ball of your foot there is less adjustment in your body from plie to relive, making everything a lot easier.

that was a lot of ranting, and i sure hope some of it made sense because i do love to help. good luck with your turning, and i sure hope i was able to give some helpful advice. heart

Edit: i forgot you had mentioned what sounds like jazz turns (turned in/parallel knee), all i know is that the better you are at ballet turns, the easier it is to get jazz turns. so if you can get a triple ballet pirrouette, there's no doubt that you could do triples and maybe even quadruples in jazz pirrouettes.