Do abilities such as lifelink and deathtouch still apply when fighting?
Yes! As all of their rules text state "damage", instead of "combat damage"
I.e.
{pit fight}
{child of night}
{Typhoid rats}
A creature with deathtouch or lifelink also works with things like {Burning Anger} and {Power of Fire}. You still gain life and destroy creatures. {Vampire Nighthawk} particularly likes these kind of cards.
Not all abilities matter though, for example first strike and double strike.