• Here's the mechanism I showed in class.  Note that the products specify an S_N2 mechanism, even though there is a tertiary carbon involved.

• Here's a suggested route to each of the products I showed.

Product 1:

• convert to alkene (dehydrate)
• add two OH groups cis (use OsO₄ reaction)
• convert cis OH to cis Br (probably the PBr₃ reaction is best for this)

• add H₂O across the double bond (anti-Markovnikov) using hydroboration
• convert to bromide
• add second methyl group using the methyl Grignard (which simultaneously reduces the carbonyl to OH)

• add Br by allylic bromination
• reduce the double bond with H₂ and Pd/C catalyst
• add methyl group as above