I have no idea if this is pushing the line for 'spaghetti posting', but i felt the claims here were so outlandish that i needed to address them individually to make any sort of sense. Please have mercy.
Current Nanotech, sure.
Stuff that is currently theoretical simply because we haven't developed it rather than because it's scifi/entertainment can go alot further. Not to mention We are talking Nanoha magic tech and Worm Tinkers .
So yes, Nanofiber mesh.
Making cells practically indestructible to anything short of acid/liquid nitrogen/star plasma can be done with Nano-ware simply by weaving carbon nanotubes throughout the cell walls. Same with bones. Add nanotubes that extrude from the cells to twist together you get super strength, immunity to crushing/slicing/puncture/tearing wounds and the cells would still be able to heal and replicate because acid is a fair part of the process.
This isn't even getting into complicated shit like healing swarms which is where the REAL complications begin. That being said, they aren't really needed in most cases.
Okay, first of all... This is... wow. I mean, even if you
could make cells indestructible (and you cant) it would be a hilariously bad idea. Which actually covers pretty much everything listed here. None of this is workable in real life, and no amount of technology will change that. Say it with me;
Nanotechnology is not magic. And there is a
wide gulf between 'what is actually possible one day' and 'shit scifi writers think up with no basis in reality'. Handheld communicators? Sure. Just a matter of size and refining the technology. Warp Drive? Not possible. End of story. Your only hope is to find a way to blatantly ignore everything we think we know about physics. Which incidentally is what it would take for most of the stuff you have listed here to actually work.
Nanotubes have a very high tensile strength for their size and you can make other materials stronger by weaving nanotubes into them, but they are not indestructible, not even close, and you cannot use them to make things indestructible. And I'm not talking about stuff like
star plasma either. The idea of coating a cell in them would just cage the cell and prevent replication, there
are applications for that sorta thing (its being pursued as a cure for diabetes to protect insulin producing cells from your immune system), but doing it to any significant percentage of normal cells is nothing more than a form of suicide. Furthermore, you need to keep in mind that nanotubes are
rigid, you cant twist them together or bend them after they are made, they can make flexible materials extremely strong at the macro-scale, but at the level of cells your talking about steel girders in a pool of jello, and they will be about that useful.
Look up Mesothelioma for how that works out.
Having nano-ware slot itself inbetween nerve connections to speed up the transfer speed would increase reflexes, coordination and thought. Get into proper medical grade bullshit and you can jump straight to super-intelligence on the low end and rewriting your brain for fun and profit on the high end, something that no other technology can do realistically without being an advanced brainwashing scheme or needing to wave WSOD in front of your nose.
Oh good god no. What people often forget is that there is a
reason nerve induction speeds are not naturally faster than they are, and that the 'gaps' between nerves are just as important as the nerve its self. You
cant speed up nerve transmission by sticking nanotechnology in the middle, youd just burn the nerve out. You would need to replace the whole nerve pathway entirely and at that point... you might as well not use nerves at all.
But super intelligence is something other technology can do... and actually really easily. Which is kinda ironic given its the example you used. Straight up virtualization of the mind can accomplish all these things without being physically impossible. Stuff it in a
actual super computer and put that in your skull. Waaaay better than anything you could
actually do with nanotech in your brain.
Biological immortality isn't out of the picture either with nanoware as aging is a function of genetic drift within the cells of the same body; as they start to become strangers you just sort of melt and then die of "natural causes". Nanoware homoginizing your genes across the body would prevent that,.....at the cost of natural evolution.
Biological immortality isnt impossible with
simple biology. You dont need nanotech for that, just genetics. Genetic drift is just one of many (and not even the primary) cause of aging. Telomere length, primordial stem cell count, and like a dozen other things all contribute, and all of those are probably fixable with sufficient genetic wizardry.
That said, natural evolution isnt much of a cost since its kinda rubbish anyway. At this level wed be deciding our own development with no need to turn to nature for recourse.
=
And, beyond all that, even if for a moment we assume you
could do all that? That every single thing you have listed here is quite possible? It still pales in comparison to what you could do with hardware instead. If you have the technology to do all that then you have the technology to build something better from the ground up and download a mind into it. All that effort, all that impossibility and the end result would
still be inferior. Anything and everything one applies to nanotech also applies to the
macro scale, and that is the true beauty of nanotech. Its not what you can do with it... its what you can
build with it.
If you can sheath a person's skin in 'nanowave' so durable you need plasma to burn them, then I can build a armoured limb made of inch thick plates of that same material, which you layered so thinly, that would be completely immune to even that. If you can create caron nanotube muscles, I can build super conductive motors. If you can engineer those systems to self repair, then so can I. If you can make someone smarter, then i can download their mind into a quantum computer.
The nature of nanotech is that the benefits scale up
and compound, what nanotubes can do to flesh is nothing compared to what they can do to a tungsten plate. While your trying to justify a nanoware transhuman... Ive built their replacements. This applies even to Tinkers and magictech. If they can do something amazing at the nano scale... they can use that same technique to do something
even better at the macro scale. Nothing that can ever be injected into a person, to change them from within, will ever be as good as something crafted to purpose without wasting time and effort trying to emulate (or even interact with) silly biological processes. As if those were something sacred and not part of the problem.
Ready when you are! 
