1. 10$, you need to buy anything that contains a half-life cd key. best bet would be half-life classic plain and simple or an expansion pack (they arent really sold anymore)
2. C-S is a mod for half-life and if you are able to play c-s online then you are automatically able to play all the other mods. there are at least 10 good ones out, take day of defeat or natural selection.
3. No, there is an anti-cheater system that bans cheaters from online-play for 1 year and they would need to buy a new cd-key to play again. also cheaters can easily be banned from servers by admins. either way there arent many cheaters around, though cheaters arent always easy to distinguish from very good legit players.
4. yes, but it gets more fun the better you get since as a good player you spend more time alive than dead. this is also why c-s is addicting and also full of nerd boxes and finally full of very good player or very good nerd boxes.
5. you always need a cd key bought from a store, just buy half-life for like 10 bucks. then download steam on steampowered.com and you can download all games and mods for half-life including counter-strike etc. (no extra money to be paid)