Translation:The teacher teaches students how to use quotes.
Hmmm. I dont think thats gonna be easy. I tried some for you but just in Portuguese :( and some of them are a bit unusual: http://www.recantodasletras.com.br/gramatica/638792 -- http://www.portugues.com.br/gramatica/regencia-verbal-.html -- http://www.netplaces.com/brazilian-portuguese/first-conjugation-verbs/verbs-with-prepositions.htm
Excellent. I found this one too http://blogs.transparent.com/portuguese/prepositions-after-verbs-part-01/
I think "prepositional verbs" was a good term to search for on google.
Good. I read "pedir (no preposition)...if you go to Belo Horizonte, you'll hear "pede Paulo ir ao banco" but where I live we say "pede para o Paulo ir ao banco. So, it may vary. Ex: sonhei com ela (i dreamed of her) / sonhei em encontrá-la (i dreamed of meeting her) (sonhar+com+noun / sonhat+em+verb). Verb+preposition is hard for everybody (like when we have to learn phrasal verbs!!) But, little by little you get through this ;)