I'm skimreading over most of this topic... Too many people creating multiple word walls .-.
Let's just all agree: Computers are good, some companies are bad, personal preference is personal.
Don't bump. It's against the rules and annoying >
http://forums.technicpack.net/threads/3-1-3-reported-issues-and-possible-fixes.30863/
Find the corresponding error here and use the fix provided. Should be solution 1 in the linked thread.
That's the one. Unfortunately, I'm not sure what the problem is here. I've seen it before a few times, but I don't actually know the solution. I have a feeling it has something to do with NEI. Can you try deleting the NEI folder from Coremods in technicSSP in the .techniclauncher folder, and see if that fixes it?
Do you really have not Antivirus? Sometimes they can impede the download. Try temporarily disabling your firewall and antivirus if you have one, it sometimes works.
The patch specifically says that it doesn't work with the version of Ic2 that Tekkit 3.1.3 is using(Not Tekkit specifically, just that version of IC2). The Tekkit team aren't leaving it out because they're lazy, it genuinely won't work.
It won't work for your server, but there is a version of Optifine which includes Multicore rendering. I think there was a thread about this, I'll see if I can find it.
EDIT: found it!
http://forums.technicpack.net/threads/request-for-multicore-support-we-needz-it.31647/
Both of your problems can probably be solved by this thread:
http://forums.technicpack.net/threads/3-1-3-reported-issues-and-possible-fixes.30863/
I know for certain that leichenengel's can be, look for the second to last.
Probably a good idea to apply all fixes.