Advice wanted?

I am located in tropical northern Australia (Darwin, Northern Territory) and I’ve recently started to fix the neglected garden of the house I rent.

I hand removed all the weeds before trying to grow the lawn and then added top soil initially. Lots of grass (and weeds) started growing very quickly. I then used a grass seed and fertiliser mix to try and encourage growth in the barer patches. The seeds have been germinating and it is slowing filling in. I have been hand removing larger weeds as well.

My questions are when should I mow for the first time and when can I weed&feed? The weeds are very hard to keep on top of and there are a couple spots which are more weeds than lawn.

Thanks for any advice.