It varies by the card room. Pokerstars security is pretty good.
Calculators are common. Though they aren't really cheating. Most of them anyway, there are some tools which are considered cheating. Same with other tools, there's lots of information you can get when using software and you have to assume other players are using them looking for any edge they can find. Imo if you are playing online you absolutely should be using either Poker Tracker or Holdem Manager if you want to seriously compete and multitable.
Collusion is also a potential issue. If you have more than one player on the table who knows what other players are holding that is an advantage. On pokerstars they have auto detection of common things there. I know my wife has an account as well as me, and it won't allow us to play on the same tables in cash games or small sit and gos. In tournaments though once in a while we do wind up on the same table.
Many of the smaller rooms have problems with bots. Though "problem" is a loose term here. The bots are generally pretty predictable and easy to play against. Often also easy to identify. Those smaller poker rooms generally don't seem to care about them as they are paying rake like everyone else and they are filling up tables. I don't really see them as an issue. They will often fold winning
hands to small raises and things of that nature. So take advantage of them.