1. Why would you even need this? As long as a mod doesn't make changes into the main Jar, it is technically compatible. Even safer if it uses Forge.
Some mods that make big changes to core gameplay, like changing completely the world generation and such, can make it really hard to play with some of the mods though, but they are still compatible in that they don't crash the game.
One exception is when a mod is based on an other, using the API this mod provides, because you need to double check the versions, or else you could encounter weird bugs.
2. Well, it depends on if the mod affects the multiplayer or nor, but most mods do indeed need to be added to both.