Looks great. Someone will love it, Hugs
As always you created something special. I do not think that there is anything to worry about as far as the double crochet. In your case. The material looks dense enough and it would be difficult to get your fingers through. The same concern has always been with baby blankets as well.
I think it's wonderful that you do this. I'd think that the care home would be astute enough to give this to someone whose fingers wouldn't go into the holes if that's a concern.
This one looks good, nice colours for a man. Why don't they like trebles - just wide enough to get their fingers stuck between them? I liked the different textures in the other one. Wonder what your next one will look like. What size do you make them? I have quite a lot of small left-overs that would be ideal for a worry mat.
Those crochet terms can be quite confusing, esp. when it does not say US or UK English. Usually a picture gets you on the right track and a chart leaves no doubt whatever the language.
It is the size of the hole. That seems a bit strange when we create loops deliberately for them to get their fingers in!
This one is about 40cm square. Working in the round like this you can stop when you like!