a reducung sugar since it has an aldehyde group

Yes

yes it is a reducing sugar, it has a free anomeric OH group. thus it can also mutarotate

Maltose, Trehalose and Cellobiose are all formed solely from glucose molecules.

Less common disaccharides of glucose include:

Kojibiose, Nigerose, Isomaltose, β,β-Trehalose, α,β-Trehalose, Sophorose, Laminaribiose and Gentiobiose.

Yes, since galactose is a monosaccharide it can undergo mutarotaion just like glucose. The only difference between glucose and galactose is the side the OH and H are on, on the carbon atom #4.

When galactose becomes a in chain form, drawn in Fischer formula the OH will be on the left side instead of the right side.

This is how you get Galactose α or β, at the end of the mutarotation the chain can link back into a ring either way, α with the carbon #1's OH on the bottom and H on top, or β with the OH on top and H on the bottom (Haworth formula).