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Some things you might want to consider:

What do you mean by time freezing? It would only be able to freeze from an outside perspective, as everything that is affected by time freezing has itself frozen and is thus unable to observe anything after the point of freezing. Similarly, if all time were frozen, then how would nature, an intrinsically time-dependent entity, be able to do anything at all, much less restart time?

Then we come to the question of how anything would be able to observe the frozen time. QM teaches us that observation requires interaction with the object being observed, but if said object is frozen in time, then how can it interact with anything?

Also, "freezing time" would only be possible in a single reference frame, since Special Relativity teaches us that simultaneity is not a well-defined concept when one passes through reference frames, so if one person sees object A and object B being frozen at the same time (which I assume would be the case), another person in another reference frame would see the freezing of A and the freezing of B happening at different times.

In terms of personal timelines, perhaps they are possible (although I fail to see why anything above a single particle in size would continue on as a unit), but anything with a personal timeline would die instantly, as life requires constant interaction with the outside world, which, as postulated, is frozen and thus unable to interact.

As for the grandfather paradox, I direct you to here.

There are solutions to the General Relativity equations that allow for closed timelike paths, i.e. regions where time goes in a circle. Theoretically one could use such a path to go backward in time.
Of course, there is the problem that the most prominent of these regions with closed timelike paths happens to be part of a black-hole solution, so anything would get sucked into the black hole and be unable to escape.

Also, quantum mechanics doesn't say anything about tiny dimensions; you're thinking of string theory, which says a lot of things but none of it is useful.

Sorry, I don't buy the John Titor is actually from the future theory (if you REALLY want to find somebody from the future, look at people playing the stock market and find the people who do the best-- if they are good enough then they're potential time travellers-- or look at people who win the kinds of lotteries where the player gets to pick their own numbers... now look at their travel records-- and so which of those people also happened to be in the right place to observe several great historical events (particularly unexpected ones such as 9/11 or the flooding of New Orleans)... those are your time travellers).

There's a third resolution of the grandfather paradox--
macroscopic quantum superposition:
The states "grandfather lives" and "grandfather is dead" are in superposition....perhaps such systems stay in superposition until an outside observation occurs and the system collapses to one state or the other (or maybe the state just naturally decoheres).... I frequently wonder what it would feel like, subjectively, to be in a mixed-state of superposition (I even wonder if I could/would notice during and/or after such an occurrence)[[I've noticed that it's important that I not take myself too seriously]].

You're probably right... but does the fact that I can simulaneously believe that you're right AND wrong mean I'm superimposed right now?