You certainly CAN seal the gaps with covering, but it's often not necessary, especially on a trainer. Wait till the control surfaces are permanently attached - if you have MORE than 1/16" gap, sealing it will give the control surface a little more authority.

As for attaching them before or after covering, have them ready to install (I.E. hinge slots cut and hinges in place but not glued) and cover. This way, you can add trim, but still take them off if you need to. Once it's finished, glue the hinges in