I play single player and on a server with work buddies. The multiplayer server isn't modded, but I like to play my single player game with some mods. If I install mods to play single player, will it effect when I join the multiplayer server?
It shouldn't be a problem. I constantly test new mods on my machine, then join my friends' server (which lacks them) without incident.
Unfortunately, the opposite isn't usually true. If your server has any mods that aren't purely XML, you'll have to have the other components on your system, too (unity3d files, icons, etc).
Depends on what mods you use. XML parts are synced with the server, so singleplayer xml-only-mods will not work on the server anyway. Other mods that are just client side however will work also on the server, e.g. the Backpack-Buttons-mod or newly the backpack-locked-slots-mod.
But to be sure, you can also simply create a copy of your whole 7d2d installation folder and put mods in just one of them. If you start the one without mods, it will be without mods, if you start the other one with mods it will be with mods. Not just practical for single- and multiplayer, but also if you e.g. want to play a total conversion like darkness falls and also still have access to a vanilla version.