What the heck is a watcher?
The Watcher’s Council is based in England, and their responsibilities are to identify and train the new Slayer in each generation, as well as to be the repository of information on evil supernatural goings-on in our realm. Giles was Buffy’s second Watcher; her first was killed.
Buffy basically recused herself from the power of the Watcher’s Council last season. Giles is her friend/father figure, so he’s stuck around in that capacity.
Does Buffy’s mom know she is a slayer?
Yes. She found out near the end of Season 3, and had a somewhat difficult time accepting it. She still hasn’t completely, but she tries. (BTW, “Buffy” fans, I made a bold prediction last night that Joyce and Giles will marry by the end of this season.)
Does Buffy bruise at all?
Unfortunately, we never get to see her completely naked. 
Angel: Is the irish guy also a killer/hunter?
Mostly answered by andygirl. Wesley is a former Watcher. He was assigned to replace Giles, who had been suspended after botching a test Buffy was to undergo. He is now, in his own words, a “rogue demon hunter.”
Does he have any special powers?
An overinflated sense of his own charm, and unpleasantly mistimed clumsiness.
Oh, and he and Cordelia once had the hots for each other on “Buffy,” but one dance and kiss at the prom cleared that up.
And why is it that between Buffy and Cordelia they own no bras?
You think that’s good, catch Faith in action on the repeats!