Question

what is the conjugate base of ch3ch2co2h?

Answer 1

Remove one proton

Answer 2

The conjugate base of CH3CH2COOH or propanoic acid is propanoate or CH3CH2COO-. Here i can kind of show the shape
......O
.....//
R-C
.....\.._
......O

Now remember there is resonance so it's a hybrid of both structures. From what you described you seem to be correct, perhaps you forgot the lone pairs on the other oxygen atom?

The conjugate acid of methoxide CH3O- is methanol CH3OH with 2 lone pairs on the oxygen atoms. So you are correct...