"can i use my bf last name for my son even were not married?"
I don't know, I BELIEVE it can be approved IF the father agree.
"can i ask for his financial support for my son even not married?"
Yes.
" and how much is it supposed to be?"
I have seen much different sums from 1000p to 4000p per month (higher when the kid is older, IF parents can afford expensive education). So I suppouse it depend of what paying capacity the parents have, to estimate a fair amount.
A bill is PROPOSED in the parlament, saying MINIMUM 30 000p for 6 months. If not paying all, then it's prison!!!
The basic IDEA is good puting pressure at them who don't try to pay fair,
BUT the AMOUNT is crazy, because most Filipinos have NO CHANCE to fullfil such amount in the long run. IF it will be aproved without change and followed, then one of the bigest islands will need to be transformed to a prison to get space for all