Painfull

Ahh okay, seeing this line : [04:03:58] [sEVERE] at InvTweaksObfuscation.getPlayerContainer(InvTweaksObfuscation.java:78) I think it is Inventory tweaks responding to it. It is already submitted at the mod makers github. https://github.com/mkalam-alami/inventory-tweaks/issues/234 It will be fixed in the next milestone probably around 1.3

Does the server start further or is that the only thing in the logs?

Well easy fix there. Do not use your middle mouse buttons in the menu. Just do not say anything whilst your starting minecraft. Have you tried it with vanilla Minecraft? If it bugs out there it is a vanilla bug.

I think it's something to do with your NEI. But what excatly I do not know. Did you change anything to NEI?

/reload breaks alot of stuff in a Tekkit server. Save-all then stop server then restart it. Should fix your problems.

ID's on server do not match client ID's

You might have a space in a place where it's not expected. Thats what I had with a server of mine.

Yep known bug, is just visual as far as I know.

Cobble gens with block breakers cause a lot of lag. Try using stuff like EE Energy Collectors and Anti-matter Relays, Much faster less lag.

Try replacing the chest. Try the quarry input into an other chest, on a other place.

Can you remember where you logged out? Then your friend can look around. Also ask if the server is 3.0.4 because that's the server version that has a big bug crushed.

Some people say Reload a few times. I say try to get Optifine out of the modpack.

Can you post the error log up until the error starts? Sometimes it gives us more info about your error.

[13:19:52] [sEVERE] Adding mods from C:\Users\Harry\AppData\Roaming\.minecraft\mods\MoCreatures.zip [13:19:52] [sEVERE] Zip found. [13:19:52] [sEVERE] Failed to load mod from "mod_mocreatures.class This seems to happen a few times. It looks like Mo'Creatures is failing to start. Which is as far as I know NOT in the recommended Tekkit build.

Also removing Optifine is also a solution.