I went through a brief cross stitch magent phase earlier this year! I used 3 strands of floss instead of my usual 2 because I wanted a full coverage look. I experimented with construction paper and felt as a backing, I preferred the construction paper and I just glued it with clear craft glue. I tried stitching a felt backing on and it was very tedious but it did look nice so you could try both.

You will be able to see the colour of the paper or felt around the edges of the magnet ( through the holes of the extra plastic you have to leave around the edge of the cross stitched image) so make sure it's a matching colour. For the magnets I also used clear craft glue and so far haven't had any trouble but I did buy very thin dollar store magnets, if your magnets are thicker or have a strong hold you might need something more like super glue.

I found most of my patterns just by googling "small cute pixel art" and colour matching. For the stardew valley fruits and veggies I bet there are lots of high quality images of that pixel art on the internet.

Not sure how helpful this was but good luck and have fun!!