I thought ьатько stands for father and тато stands for dad
I thought so as well. I missed this question because I selected only the "dad" option instead of the "dad" and "father" options.
Past lessons accepted батько for dad, but this one does not. Why not?
Why doesnt вареники in мій тато їсть вареники з капустою have the -у ending since its supposed to be in accussative form
Only feminine nouns change endings in accusative. Since вареники is not feminine it doesn't change. I think you can verify this in Tips&Notes for Accusative.
"вареники" are in acc (їсть що? (what?) вареники), капуста is in instrumental (вареники з чим? (with what?) з капустою)
Should be tato for dad.