Yes, optifine.net
Lots of mods do not need forge, big ones such as: OptiFine Too many items and Better Sprint (all i know of)
Forge Modloader is how the mods are loaded into the folders of Minecraft, as you can tell in the name. Why can you not use forge?
Optifine is only required for HD texture packs; it is not required nor necessary if you don't use/have any installed to your texture packs folder. ModLoader/Forge is needed for some mods, but not all; it's best to consult the mod's topic and read the requirements to be sure whether or not the mod needs either mod loader installed.
Donate to optifine, or buy minecon tickets. (I have a optifine one)
You go on custom games(not forge) and select a map and you're on without forge
No.
Yes you can download them together however these two have some bad history together and when installing certain mods with them both installed may cause error, just a heads up.
For HD texture packs (over 16x16 in resolution), you have to use either MCPatcher or OptiFine in order for the textures to work and animate correctly.
Optifine is completely free to download. If you need help installing it look up youtube videos how to install it
Yes. Optifine can count as a mod. Just place your optifine.jar in the mods folder, and add other mods with it.
you get forge automatically without any mods
use a 64-bit java to run minecraft. Or install optifine to reduce lag