It's asking you to launch Steam, not Skyrim. You must have Steam running in the background before MO will launch Skyrim for you. You have to launch Skyrim through Mod Organizer for your mods to show up, because MO uses a virtual file for your mods. Mods are not actually placed inside your Skyrim Data folder with MO like they are with Nexus Mod Manager, so if you launch the game outside of MO, you won't see them in game. SKSE is a script extender, and for certain mods you do need it, but not all mods require it. The LoTR Weapon pack will work just fine without SKSE. It's for mods which require expanded scripting, like Frostfall, for example. I'd really encourage you to watch the video series veen21 posted. As well as this one, also from Gopher, on Mod Organizer. He explains everything thoroughly and has taught many people how to mod with his videos, including myself. :)