Actually, the title says it all…
Yes you can.
And how?
What do you want to install?
Because with me e.g. Not the questbooks and the start items as it should be in the packs
Yes. Either go to Curse Forge (those who work with Twitch) and just download them without Twitch.
Otherwise there's the "Technic Launcher", but I'm no longer quite sure whether it is still used often.
Yes you can
I would generally not install mods via Twitch
Yes, of course Minecraft is not in copp with Twitch