ok, your computer appears to be posessed or something
the itunes installer problem, nfi whats precisely causing it but a google search came up with a similar sounding error for a different program installer - in the faq for it they blamed it on corrupted fonts that were installed by hp printer software. If thats the case for you i have nfi.
the computer not shutting down is probably related to the cpu usage on system, its waiting for something to terminate which never does.
Not entirely sure why the image preview is broken, but it may be some system files are borked.
try a "sfc /scannow" from a run prompt to verify system files are intact.
when the internet drops for you, can you still resolve names to ip addresses? try a tracert on google or something the next time it happens.
Any other computers connected to your router, test it with those as well so you can narrow it down to either a computer problem ( most likely ), or a router problem.
check theres nothing running which shouldnt be, spyware/rootkit/etc which might be messing things up.
personally i would do the reformat/reinstall route, theres a lot of problems which may or may not be related to each other and its likely just easier to wipe and start again