"I hold a bag."
Random question: why is 'kaban' ("bag") written in katakana- カバン? Is it not a Japanese word? (It even has its own kanji- 鞄), so I don't understand...
I'm not Japanese so this may not all be correct, but there are just some Japanese words that most people prefer not to use the kanji for anymore, and use katakana or hiragana for instead. For many of them it's because the kanji were too complicated or it was a purely phoenetic kanji reading. In this case, it's because the kanji isn't usually taught in school; It's not part of the 常用 (jouyou) kanji.
It's a jinmeiyô, so high schoolers should have learned it. The reason why it's in katakana here is that it's less formal, at least accoring to good ol' Wikitionary.
Is this a universal "hold," or is it specific to certain things? I.e., can you use mochimasu for things like food, clothes, babies, etc?
for reference, this is not true, a lot of people also write it in katakana too, this happens with a lot of nouns that have kanji that are not part of the Jōyō list as 鞄, and also with luxury items.