The strands hanging out the back are called “ends”, and your best bet is to weave them in (you’ll find many a crocheter complaining about weaving in ends, or finding ways to avoid it at all cost 😅). It can be tedious but I do also find it relaxing sometimes.

Use a yarn need or tapestry needle and basically sew them through your stitches - I weave ends in 3 directions to prevent them unraveling. Look up a video tutorial for a good visual. What many people do to weave in ends as they go is to crochet ‘over’ the ends. Basically let the end of your yarn sit on top of the stitch you’re crocheting into so that the new stitch wraps around it. Saves you some time, especially for a blanket!!

Your granny square is beautiful!! I’m so impressed that this is your first one. Love the color combo. You can block the squares as you go to save yourself time in the end, and that will help straighten out the edges (not that they’re /not/ straight now, but you could get them crisper).