"I put the postcard in the envelope."
This is confusing because you could say either 入れた or 入れました and either would be correct. Sometimes you guys use keigo and sometimes you don't so it's really hard to tell which one you're supposed to answer.
The ます form is pretty much always accepted, so if you're unsure, go with that.
An easy way to think these "something in something else" sentences is to just reverse the order of the english words. So if I put an envelope in the mailbox, the mailbox would take higher presedence and there for be first in the Japanese sentence. Think of the holder of the object as a higher priority.
Could someone explain the use of katakana for words such as カギ and ハガキ that seem to be Japanese in origin as far as I know?
We use katakana for animal/plant's name. Apart from that, it is customary, i.e. cannot be explained.
Yes the examples you provided are of Japan origin, and the followings are examples commonly written in katakana.
- 葉書（はがき） postcard
- 鍵（かぎ） key
- 餓鬼（がき） brat
- 塵（ごみ） rubbish
- 皺（しわ） wrinkle
- 癖（くせ） perculiarity
- 駄目（だめ）no good
- 喧嘩（けんか） quarrel
It's more of a matter of を going with ハガキ than one going before the other