yes and yes.

I've had up to 7 broadcast centers on one planet. In areas where enemy culture is high, I routinely build 3.

The more trade ports you add, the more trade money you generate, but its increasing the number of ships, so in a large game, too many trade ports can start to create a lag issue.

A trade port generates income, but its long strings of trade ports that generate the most income.

So 4 trade ports on separate planets is probably better than 4 on 1 planet. Cant say I've tested that tho.

I generally dont build a trade port until I can put 2 or 3 in on adjoining planets.