Residence permit for TCN with a child - partner of a Maltese

I'm Russian, my boyfriend is a Maltese living in Malta. We have known each other since half a year and want to live together in Malta. This is still too early to think about marriage, but if things go well, we will marry in the future.

We've checked with the Immigration Office and the only option for me to get a residence permit would be to apply as a partner of a Maltese. As we know each other for less than 2 years, they've offered a 3 month resident permit with a possibility to renew.

The list of supporting documents is quite straightforward, but the procedure is not clear for my 2 years old son from previous relationship. We were told to bring his birth certificate translated. I'm the only parent and his father's consent is not applicable. Do I need to fill in a separate application for him and he will also get a plastic residence card?

We first came to Malta for 22 days in September on Shengen visas type C (single entry), the second visit will be in November on Shengen visas valid for 23 days (single entry). I don't think they will issue the cards in 3 weeks, so what is the legal way for us to stay in Malta during the application process? Do we have to leave and come back on a new Shengen visas or try to apply for a long-term visa type D (national) at the Maltese Embassy in Moscow?