wrote:

Q1. When the plantlets have become established, should I leave them in situ
to over-Winter or should they be transferred to the coldframe?

I transfer them, that way the 'old' strawberry bed, gets a good clean
up, they are 'heeled' into spare patch of ground, and let nature look
after them :-)

Q2. Next year, will the parent plants still be capable of producing good
fruit (in the planter)

Most strawberries fruit better in second year, as long as you have
good size planters.

Remove almost all the leaves from the 'old' plant now, lets the light
onto the enter of the plant and produces a better crop next year.