Can I attack with a Pokémon if I just played it?
Yes, as long as it's your Active Pokémon (only your Active Pokémon can attack) and as long as it has the required amount of Energy for the attack.
Source: WotC Chat (1999-09-30)
If I attack with Venonat's Leech Life and do 10 damage, how many damage counters do I remove from Venonat?
You remove one damage counter, which equals 10 damage.
Source: WotC Chat (1999-09-30)
When I attack, do I discard the Energy card(s) I used to power the attack?
Energy is not used up by an attack. Unless that attack specifically says to discard an Energy, it stays attached to the Pokémon.
Source: WotC Chat (1999-09-30)