Wow, jesus. Not to be a dickbag (A bag of dicks) or anything but I'm pretty sure you just (I don't know what it's called) posted 5 times. mmuziek, use the edit feature, copy the logs from pastebin into error logs rather than the link, and you can just edit the posts that only have a few messages in them. Not to be an asshole but you might want to read through the rules. If someone other than me sees your posts they'll probably report you, I'm just trying to be helpful here.
Now onto actually fixing things. Close any non mandatory (fancy word for non-essential(fancy word for not needed)) programs. Those might be using up some memory so your tekkit can't allocate enough. And from what I can see it looks like your Technic Launcher is redownloading every mod every time you launch it? It could be that due to its constant redownloading of files your internet is slowing down. Also there's a bunch of Java errors going on in there that I don't understand. Try uninstalling Java 6. Your technic launcher is using Java 6 instead of seven. If none of these work and if nobody else posts here in a while try deleting .techniclauncher and downloading everything again, after you uninstall Java 6. Then make sure it's running on Java 7.