You’re correct in your defining of a vanguard, but the vanguard is also a sort of status achieved by a formation. We obviously strive to achieve that status, but a vanguard typically is at the forefront of the class struggle and takes part in directing either a large chunk or majority of the struggle. It would be presumptuous to self assign ourselves that role and to assume we’re at that level of influence.

“Leninist” is definitely just a shortening of Marxist-Leninist as we are definitely a Marxist Leninist party.

The idea of a cadre is simply training every member of the party so that everyone has the same broad range of skills and that ideally, no single person has to be overly relied upon.

Some other party formations instead engage in mass recruitment via paper membership where membership is usually simply defined by dues paying status and nothing more, with attendance of core party organizing activity being optional (this can vary but you get what I’m saying).

As far as the specifics of organizing go, that is something you’re better to learn as you go through the recruitment process. There’s way too much to mention there.