Thanks for the large report. We generally prefer one issue per report, though. Also, most of these have already been reported; feel free to vote for those ones:
Feature requests should be posted onto /r/MinecraftSuggestions, not here; the tracker is for bugs only. Those are both fair suggestions (though you're not the only one who's suggested them).
The walking sound is not in sync with the players walk frequency in 3rd person, but in first person the screen bobbing is just right. Perhaps change the speed at which the legs & arms move?
I haven't noticed this one, and I don't think it's been reported. It does seem more like a feature request though. (I actually didn't realize that the bobbing was aligned; this'll probably bother me now 😃)
Walking on carpets makes the sound and running particle effect of the block underneath it.
This is MC-8820, but it's fundamentally caused by the next issue...
Running near water shows the sprinting particle effect coming from the water. This just looks cheap.
This is MC-1133, and it's rather hard to fix unfortunately since it's a fairly deep issue in the engine.
Small, thin floating lines and gaps in the corners appear on a person's character model and tools they are holding in both first person and third person
Thanks for the large report. We generally prefer one issue per report, though. Also, most of these have already been reported; feel free to vote for those ones:
This is MC-88356.
This is MC-86127.
I think this is MC-74764.
Feature requests should be posted onto /r/MinecraftSuggestions, not here; the tracker is for bugs only. Those are both fair suggestions (though you're not the only one who's suggested them).
I haven't noticed this one, and I don't think it's been reported. It does seem more like a feature request though. (I actually didn't realize that the bobbing was aligned; this'll probably bother me now 😃)
This is MC-8820, but it's fundamentally caused by the next issue...
This is MC-1133, and it's rather hard to fix unfortunately since it's a fairly deep issue in the engine.
This is either MC-73186 or MC-1794.
This sounds like MC-86253, but that was already fixed. It might also be MC-82995?
Not entirely sure what you mean by this, so I'm going to go with 5.
In general, these are all valid bugs, but they've already been reported. Please search first, and try to stick to one bug per report, thanks.