Here is another view of the yard/grass.

And one more, last one..

It is Bahia, I can tell because in the photos you can see the black V seed heads.
I will guess you live below the mason Dixon line or if in Cali, south of SF.

I just reread your post, your in FL. This is an OK low maintenance grass. No need to fertilize, but if you do, it will grow fast and need to mow twice a week. If you leave the seed heads on for over 2 months they will become viable seeds.
You can use 2,4-d as a herbicde. Metsulferon will kill it, along with many other herbicdes.
I would suggest to self install an irrigation system. Then decide what kind of grass you want. Many people in florida have Bahia for lawns. If you keep this as your lawn, I will suggest that you mow it high, 2-3 inches as this type of grass is an open grower. The lower you mow, the more sun gets to the soil, the more weeds you have. My house had this when I moved in, I installed irrigation, killed off the lawn with round up and plugged an empire zoysia lawn.
I would suggest that if you do not like yard and lawn work, keep the bahia, if not, I would look into bermuda (princess or riveria), zoysia, and last, if you have no traffic in your yard (dogs or kids) and you like the spongy feel go with SA.