You cannot get earned income credit or education credits if you file married filing separately--so please clarify what you mean by "ex" and "separately." If you are still legally married you have to file MFS or MFJ. If you are divorced as of the end of 2019 then you file as Single or Head of Household, depending on who has custody of the children).
If you are divorced then the custodial parent can sign form 8332 that allows the non-custodial parent to get the child tax credit. The custodial parent can still file as HOH, get earned income credit and childcare credit. The custodial parent is also the one who gets education credit.