I'm a n00b, I need some help!

[MunchkinMan]

Your friend was correct. When a player faces a Monster, he has been in combat, even if the Monster won't fight him.

As for specific issues: A monster that won't pursue means that it won't chase you if you have to Run Away. You still have to fight the Monster, but you won't suffer Bad Stuff from a Monster that won't pursue you. A Monster that won't fight, however, will leave the combat.

Finally: Unless you die, combat ending does not automatically end your turn, even if you lose that combat. You're still allowed to do any turn related actions before you decide to end your turn.