I am working with exiting solid core 12 gauge on light fixtures is a basement.

Can I connect stranded 12 gauge to the solid and then connect the stranded to the light fixture?

Do I need to crimp a terminal on the stranded end going to the fixture?

Wire nuts, or marretts in Canada or UK will work fine.

Each are listed for different sizes and combinations. See list on carton.

Absolutely. Very often the majority of commercial wiring is done with stranded, and solid is pigtailed for receptacles and/or switches.