Launcher...log. If you get a whitescreen, you have one. If you ask where to find it, you didn't read the Common Problems and Solutions sticky, or didn't read it closely enough.
I'm guessing the rubber tree farm or some component of it is dumping stuff all over the ground. Try "remove items -1" from the console and see whether it clears up the lag. If it does, go look for loose pipes (anything that fills a chest and starts spilling, or what-not).
Yeah, at least one of those will block users that don't have OP ([buildcraft] is one of those) from modifying blocks, which the quarry is trying to do.
Yeah, don't bump, unless you're adding content. These are both client-side mods, so...I don't really see a way to get them to not reset when you update the client.
Minecraft is not one of those programs. You will have to manually select the version of Java that's appropriate by running the launcher .jar with the full 64-bit Java path.
Sorry, but I haven't found a way to pipe anything into that second slot - it seems to be manual-load only. Your best option at this point is to just run it through an induction furnace twice.
GUI Scale is set in the Video Options. Normal or Small usually show the NEI interface if it's there, while Large may not. Just maximize the MC window to play in "full-screen".
This was a 3.0.3 server bug. Make sure you have 3.0.4 installed. The suggested solution should fix the problem, but make sure you back up the world and any alchemy bag/tablet data you want.
The error log doesn't pop up on your desktop. It's in your .techniclauncher\logs folder, which you would know if you were paying attention to the bug report form.
Also, using 32-bit Java with a 64-bit OS is asking for trouble.