I just tested this myself, and I didn't have any problems damaging the frigate or progressing through the tutorial. I don't know why you're having this issue. What I can say is that you're basically at the end of the first tutorial anyways. The only step left is to order your units to the next planet, kill the defenders, then bombard it with your capital ship.
If this is your first RTS, then I can understand wanting to play the tutorial through. The fact that you figured out how to toggle auto-attack on your own tells me you have the right intuition, though. I think there are really only four things you need to understand to be able to jump in and play a full game:
- How to purchase planetary upgrades (particularly population upgrades) and their importance
- How to build new units and structures
- How to command your units and capital ships
- How to research new units and structures
You can figure out the finer details of how to use each unit and structure as you go, and you can always ask questions here on the forums. I'm kind of the resident strategy guru and can help you with these sorts of things if you ever run into a roadblock. When you do jump into a game, I recommend a 1v1 on a randomly generated small solar system against an easy AI with the pirates turned off.
As a rule of thumb your priorities are to maintain a larger fleet and larger empire than your enemy. It's okay to let your tech level slide a bit; you can recover from that if your other fundamentals are good. However, if your empire is small and your fleet is weak, no amount of tech or development will save you.
Happy hunting, hope you enjoy the game!