What am I to do when something appears on one of the levels?

I own the game (on Steam, not even sure if a retail version exists..). The popup messages like "small rock has appeared!" notify you that you've unlocked an acheivement, that's all. Some acheivements have rewards, though.

I'm equally confused about the bomb message, though.

What Snailer said is partially true. Some of the popups are tied to achievement. However, all the popups that say "... has appeared in the basement" is new content being unlocked. Mostly these are new items, and mini-bosses that you can find in the latter play throughs. Like the message you got, would mean that the item "Small rock" has been unlocked, and can be found further down in the dungeon, or in later play throughs.

Regarding the "Bombs are key" - that's actually the effect of the pill you took. Each color of pill has a random effect in each game (like potions in most roguelikes). Most of the messages are much more self explanatory - "Range down", "Damage up", "Full health", but there are a few weird ones. "Bombs are key" in particular is odd - it swaps your current count of bombs and keys.

mordi2k's answer is right about the other stuff.