The month of April I got an eviction notices to vacate on the 9th. I gave the rent office 900 dollars on the 17. After do so I got a court day to not pay of rent for April. Now I do owe them more money. Is they allow to still take my money and still take me to court?

Yes. They are allowed to take you to court unless all rent (including June) is paid in full.

Were they paid in full of all money that was owed them ?

Paying 900 dollars if you owed 2000