vermeiden and meiden, antworten and beantworten, and similar
Are there any rules about these?
As said before, but a bit more general: vermeiden is used with actions, meiden is used with objects (things, geographical areas, persons). (NB: we also say "Müll vermeiden", but we mean to avoid the production of garbage, not the garbage itself. Meiden is rather keep away from something or someone)
Antworten is used with the "inquirer" (in dative, e.g. "Ich antworte Dir"), beantworten (or also antworten auf) is used with the question or the mean by which it was transported (call/letter/email) in accusative (e.g. "Ich beantworte deinen Brief" or "Ich antworte auf deinen Brief").
I hope that counts as rules....
Ich meide das Gebiet/deine Nähe. Ich vermeide es, dir weh zu tun.
Ich vermeide es, Fleisch zu essen.=Ich vermeide den Konsum von Fleisch. ≈ Ich meide Steak-Restaurants.=Ich vermeide den Aufenthalt in Steak-Restaurants.=Ich vermeide es, mich in Steak-Restaurants aufzuhalten.
I recognised that it is really hard to explain. Maybe like this: "vermeiden" is used if an action is avoided. "meiden" is used if the contact to a thing is avoided. I am not sure if "meiden" is only used for places as in all of my examples.
You also asked for similar words: aufschreiben-write down; schreiben-write (ingeneral)
brennen-burn (Das Haus brennt.-The house burns.), verbrennen-be destroyed by fire(Das Haus verbrennt.-The house burns down?)/destroy sth by fire(Ich verbrenne das Haus.-I burn (down) the house.)/sich/jemanden verbrennen-hurt oneself/somebody by fire (Ich habe mir die Hand verbrannt.-I hurt my hand by fire.) Also exists "abbrennen" and "ausbrennen"-burn so long that fire has no more material/energy to burn.
(zer)schneiden, (zer)reißen, (zer)brechen, ingeneral verbs about destroying can have the prefix zer-. But I'd like to go to bed now...