1. Do recruitment firms mostly help international firms in the hiring process? I understand most local firms recruit directly but I might be wrong.

Most international firms hire directly and via recruitment firms. I will say, though, that most of the time when they hire - they already have target people in mind, or otherwise a small (very small) target group of people. You will usually know if you fall within the target group - whether by way of a direct call or through your network.

2. How do people start knowing about which teams are hiring besides hearing from their own networks?

no other way. make friends. fast.

3. How far in advance do partners start to recruit?

they hire when they need the headcount (not in advance), unless its a new team in which case they will most likely just poach the entire established team as opposed to a single person. unless you damn zai.