I'm installing a dimmer switch to replace a wall light switch (in the
USA). The house was built in the 1960s and the junction box is metal
and grounded. However, the ground wire from each cable (NM romex
cable) entering the box is connected directly to the box (no pigtail.)

The new dimmer switch has pigtails, including the ground wire. Is it
ok to connect a short green (stranded) wire to the box, and then use a
wire nut to connect this to the green dimmer pigtail? (Today, normal
practice is to connect the ground wire from each cable entering the box
to a wirenut, then use a pigtail to ground to the box, but this is not
possible with my existing wiring.)

Also, the dimmer pigtails are stranded wire. Is there a recommended way
to connect solid to stranded wire in wire nuts?

Thanks!