I'll jump right in and maybe sound rude, but I don't mean to be:

1. WHAT grass?

2) is this your first winter in FL?

HostaHeaven, I'll bet you came from that Land Where Hostas Grow. I've heard of that lovely place. And the cold and snow.

Pic #1 ? If it stays small, leave it. If it is fast spreading with a tap root, pull it before it blanket's the area. You'll know the difference. The obnoxious one usually starts to take over in summer rainy season, so if you haven't seen that one yet, maybe just keep an eye on this. Or, maybe it's setting your yard up to expand next summer. Help! WHAT IS IT?

Pic #2 Dayflower (Commelina diffusa). Green with tiny blue/purple flowers... what's not to like? And you didn't have to plant it!

#1 rule of lawns in FL: If it's green, mow it. That's your lawn.

Pull the first one leave the second. The first one looks like the babies of a bur plant...it has pretty flowers but then it has burs...burs that cling and wrap and make more bur plants.