We have some time and budget to fix/customize before move in date and I want to ask for some advice/suggestion.

This courtyard is pretty small. This is how you walk into the house. Courtyard, sliding door to living room. In picture it looks pretty big but it's actually about a size to put a ping pong table (and to play).

We have two little boys(1 and 3) and we don't wear shoes in the house. I was thinking about putting fake grass or deck like material(wood). So this space blend in with indoor. And have boys run around the house in circle. And have outdoor cushions so they could lie down and see the sky/stars. And replace the two big sliding doors with roll up/fold up door. Does it sound feasible? Would be doable for 10k?

House has pretty decent size backyard so I could add this deck to backyard as well. Any suggestions?

Ping pong table was my husband's suggestion. Or maybe a fake tree with christmas light so it would look nice at night from every room in the house?