Filling for My Mother's Immigration

I'm a US citizen wanting to fill for my mother who also has a 3year older daugher(my half sister)
My question are as follow
1. Do I need to fill out two forms one my mom and the other for my sister. Or
2. Does my sister qualify under my moms application since she's a toddler(under age). Or
3. Will it require my mom to come to the state first and file for my 3 year old sister
4. Can I also turn in an application for my adult brother and what is the processing time for siblings.

Priority dates for the various categories are updated monthly in the Visa Bulletin on the State Department website.

You half sister does not qualify under your mother's petition. If you file for your mother, your sister must remain behind and your mother than then petition her as the unmarried under 21 child of a permanent resident. Otherwise, you can petition her as a sibling as you can for your brother and when her priority date is nearly current, petition your mother.