Translation:He kisses his girlfriend in the forest.
Like koramikínon, also in compound words the stress always goes to the penultimate (last-but-one) syllable. The secondary stress is on kor- in this case, so: kòramikíno. In real life, though, people sometimes stress kor- more than the -ki-, simply because it also comes rather natural to emphasize the modifying part of a compound word.
Thinking of "sia" as "his/her/its/their own" is fine as a memory device. But it is not the translation.
"He is seeing his own girlfriend and that of his brother" > "Li vidas sian propran koramikinon kaj tiun de sia frato."
Actually, you could use "his/her/its own" in the subject:
"Their own cat is brown" > "Ilia propra kato estas bruna."
"His own girlfriend is there" > "Lia propra koramikino estas tie."
A comparison or contrast is implied to some other cat or girlfriend.
On the contrary, "sia" refers only to the subject, thus can't be in the subject.
The meaning is, indeed, that the girlfriend/cat or whatever is the one of the person, thing or entity mentioned in the subject, but there is no emphasis like when adding "own" in English.
Both "wood" and "forest" can be translated as arbaro, and that's the word commonly used for both. If you want to explicitly specify that it's an especially big forest, then use arbarego, but that describes an especially big forest... like in Siberia or Amazonia. If it's only a small forest, then arbareto.