YouTube once accessed, then gradual iTunes shutdown & iPad slowdown

Question

Seems to be a popular issue lately, so I assume apple is working on it.
My account:
First noticeable issue was when accessing YouTube to watch a clip from the DNC, & it took forever to play. One month ago I downloaded the first GOT season to see if it was anything like the books, & the downloads kept slowing down a bit. The blue track bar during video would halt, stop downloading, or not play through once download complete. So then I decided to be patient & wait for my downloads to finish before viewing. Well, the DNC clip wouldn't even load. 30 seconds (+/-) of pay and refused after that. That was 2 days ago.
So within 2 days it kind of manifested like a bad illness. As in, no issues for the last month since overdosing on Game of Thrones downloads, then I stop by YouTube for the DNC & here's the order of frustrating failures:
Pending iTunes purchases just aren't downloading.....last night I even "watched" as it loaded 1 megabyte every 5 minutes. I can't get through to YouTube at all. Emails are crawling in. "you do not have permission to access the requested resource" pops up when I try to play a video that I bought from iTunes that was fully downloaded, an episode of top gear. I was able to watch the half downloaded episode last night, until the download started crawling, but not today. I can't even update any apps or download them either now. I tried to download the USAA app, and it just sat in waiting status for a day. Then I thought to try an update on an app that won't break my heart to lose, & thus eBay was my lab rat, & it just refused to download.
My response was to shut down & restart, I can't say how many times. Each time, varying the length of time it was shut down, up to an hour. Then I started deleting videos & apps like crazy, clearing another 10 GB of space, since I put MSCL in the cloud then I can pull it out later, like all of these iTunes purchases that I previously backed up.i even cleared out my bulk & trash folders in mail. Then I went to settings, cleared safari history & cookies if that was involved, then went to diagnostics........the iPad has sent more reports in the last 2 days than it has in the last 6 months when I bought it (3rd gen). The only diagnostics, actually (I just pulled it up to review) prior to the last were a couple of "low battery" reports. Within the last week (per the date stamp in the header) the reports have been: a long series of "awdd_2012-09-0X........" and the time stamp & the rest of its own code; about 20 app crashes headed by "Latest Crash-iBooks....." or Facebook or anything; FaceTime; "hog_2012-09-06......."; "mobile mail & date etc...."; and "log-aggregated-2012-09-06......".
Randomly the apple Id login would pop up, usually delayed after I started a download. Came up 3-4 times, I rejected the first few times but by the time I actually consented it was already really obvious that the iPad was having an issue with data moving slower than cosmic development, & it was likely to complete something I initiated. Knowingly at least.
No issues with latest version of iPod touch, but that doesn't get as much action as the iPad.
To be fair, I don't access questionable sites or open questionable emails, I'm a pretty safe consumer & not too curious about what's on the web, but it's just something I think you can't ever be too secure with. Top corporations with big deal security still get hacked, I'm not a remarkable target like that but for sure an easy victim. Either way, I don't think it was anything out of the ordinary that I did to bring this on. I really think it was when I accessed YouTube, & a lot of posts say the same thing. MY reason for writing so much specifically was because it went beyond that & even beyond the iTunes issues to the point where it's slowing everything down. Yesterday was the first time Ive ever seen a sending status bar for an email, a one sentence email. At least in the last 15 years, for sure.

Answer 1

Yes, I'm out of warranty period.
No, i wasn't practiced a regular shutdowns. I'm exactly like you was able to go months without restarting or shutting down my pad. Except of occasional miss of battery recharge.
No, i am usually do not restart my device if apps do not ask for it (and they usually won't).
First time at all i noticed the problem when forgot to put iPad on recharge and found it powered off.
I thought i was unable to start it because of empty battery, but then, issue repeated when i was aware that iPad still had more than half of battery charge.
Later i noticed that iPad did random shutdowns by itself. By that time the only way to power back my iPad to home screen was [home]+[power] combination.
Now it even after a fresh restore being empty factory reset, iPan fails to start to home screen starting to restore mode.