In my knowledge birth control is permissible in Islam. I have a Muslim brother who endorses condom, when someone question him judging it is non-Islamic, he jokingly said that i didnt tell to use it to other than your wife.
I dont know about the high birth because many non Muslim countries like Philippines have dozens of children,
So in short, it is very difficult for a man to marry, if he is unable to offer dowry & later support his wife, one is suggested to fast
Same case with children, it is big responsibility.
Now that I am married, I still fear to have child yet because I might not be able to give enough time etc.
ISLAM is easy religion and there is no compulsion in anything, ISLAM is also flexible but not changeable.