Who am I and can I use Houses derivation as the one who asks?

I know asking person (me) usually is signified by Moon. However, when it comes to relationship and romance (7th House) a woman should be the Moon and a man - Sun. 1st H ruler of Gemini is in 6th (Mercury) and her 7th house ruler of Sagittarius is Jupiter in 10th.

So what are my significators? Am I Moon and Mercury or Sun and Mercury are my co-significators?

You are Mercury and the Sun with the Moon as co-significator. Only use the Sun and Venus in relationship questions unless being used as the main significator.