Should I TM away Ancient Power on my Rayquaza

If it's working for you keep it for now. Ancient Power Ray is not a bad choice with Lugia's weakness to rock.

Let's say two scenarios: If you want to contribute maximum damage to Lugia in a group with limited trainers(let's say 7 or so) to acquire a higher chance of capture with +3 balls, Ancient power is totally not enough to achieve that goal (As the other trainers will contribute a lot more than you do because there are much better options that are easily accessible like tyranitar) and you could only acquire +2 balls generally. At this point, Rayquaza is not a good choice to against Lugia.
Another circumstance is that you join a public group with more than 15 trainers with only +1 ball and you don't care about it. Then you do not need to TM.
So generally, it's all up to you. However, I think Rayquaza is not a good option.

Yes you should, the move is pure garbage save for a few niche cases.

Outrage is better against Lugia than Ancient Power, so if you have the TMs, use them.

Rayquaza is also far from the best counter. Even level 30 Jolteon is strictly better than a level 25 Rayquaza, not to mention the obvious top counters Raikou, Zapdos, Mewtwo, Gengar and Tyranitar.