Firstly...
Play one skirmish game (you don't even need to finish it. Just look at all the abilities and play around with the DG a bit) for every DG in the game. It's a trillion times easier to fight a DG when you know what is at his disposal.
Secondly...focus your build and get gear that complements it. You said you're getting minions and skills that heal/support them. I hope you're not spending all your early cash on the minion idols and then having nothing left over..because if so, that's an easy way to die to any DG that tries to fight you directly.
I don't know how to play oak...but as Sedna, I get monks right off the bat, and for awhile, those + yetis comprise my minion force. My money goes into getting whatever gear I need (Which depends on the game, but you generally will need some). I only get other minion idols after I'm sure that I have enough armor/health/mana/etc to be competitive. Don't blow all your early cash on minions, or your DG itself will be too weak; I only get other minions when I have spare cash.
1) Never, ever fight against 2 demigods unless you have someone with you.
2) Do not chase into tower range, particularly at earlygame. This will get you absolutely friggin wrecked the vast majority of the time.
1 is good advice...most of the time, but not all of the time. Depending on the situation, you may be able to survive such an encounter and do some damage, or you may be able to hold off while teammates come to you.
2 depends. You will many times be able to kill off a DG. Even if you die afterwards, unless there was another enemy DG there, they wont get gold/exp for your death...but you will from theirs. Err on the side of caution, though.