1. Are the greyed out dots unowned SCs even though their territory is colored, so should I just consider them neutral?

Yes, the grey dots are neutral/unowned, even if the territory is coloured.

2. Can a player controlling more than one vote cast those votes for two or more different coalitions ?

Yes, but not for the reason you are asking.

Players can cast their votes to as many coalitions as they want. They cast their votes as a group, the votes are not divided up. So a player with four votes to coalitions #1, 3 and 5 would cast all four votes to the three coalitions listed.

2b. So what you are saying is that if I e.g. have 3 votes and vote for 4 coalitions, they would all get my 3 votes instead of 0.75 vote each?

Correct!