I'll try to answer to all your questions but please calm down first....
Your activation should be done on the next 24 hours and hopefully at the time of your Lan...
The cheat itself can be used on the Lan depending on what AC your Lan will use... (VAC and All Server sided AC aren't a problem). And no. You don't need an USB stick to inject the cheat, in fact, u shouldn't use one, not just because it's stupid, but also because it's squetchy as fuck to have something luging to your PC on a Lan...
And I don't recommend you to use LC at your Lan cause this is a cheat that requires time to master unless you are already studying wiki and learning how to configure and use the cheat.... Still, I don't advise you to cheat at your LAN with LC since you are new and you will probably fuck something up....
Multi league will support the same as non multi at this point of time, BUT, if you are planning on a long time usage of the cheat, you should consider to buy Multi league version , so that u can have a 2 month usage of LC and u can be able to buy PRO version, when LC 3.0 come out with Faceit Client support, EAC, CEVO, GC..........
Hope I could answer your questions and have a nice day sir...
@ToX @sebus1315 @Apache if I missed something please correct me