I'd tend to mix the MP with a JIno3 type- John Innes. The latter is more suitable for permanent planting, but by mixing it with some MP say 50/50 it'll be a 'lighter' mix.
Alpine strawberries cope with quite poor soils IME, but anything grown in a container relies on us to feed it as & when.
Agree with Geoff, they will need feeding. Initially I'd add some slow release food pellets at the time of planting up the container. Those dont last for ever & a high potash feed, as for tomatos, will help promote & keep them fruiting.
Annually I'd feed the container in Spring & either add to, or replace the top few cms of compost to give the plants a boost. J.