Those plates on the transom look like some sort of reinforcement put on by a previous owner. They are definately not factory. Probably installed to make a weak transom seem solid. As to the floor being solid that can be acomplished pretty easily by laying new plywood down over a rotten deck or stringers (The support structure for a boats deck). Then covered with new carpet. It's a patch job that can hide major damage that will be expensive to repair. It is entirely possible someone redid the deck without redoing the transom as that is how our Starcraft was when we bought it. On an alluminum boat like our Starcraft the transom is reasonably easy to replace without removing the deck, but on a fiberglass boat like that Glastron I'm not sure it's doable without ripping out at least the rear of that "Solid Deck".
I certainly wouldn't pick her up put a motor on her and take the family out for a ride without doing some serious investigating on the transom and the structure under that deck.
As has been stated above their is very rarely such a thing as a "Free Boat" most of the time , unless it's coming from a family member or good friend, your picking up someone elses project that they've given up on. If it's free then someone has really thrown in the towell, and is willing to take the loss of their time and money. That's not usually a good sign.
Seeing that it is missing the controls and motor this could have started out as a project for someone and then turned into a donor boat for a better project. The important thing is you understand that to redo a boat that has bad stringers or a bad transom, usually both, is expensive and time consuming. Estimates on materials alone could be as high as $3000.00, and that's with you doing all the work.
As far as time goes We have a 20ft Stratos ski boat in our garage that has been in drydock so to speak for 2 years this month. It's not a project we're in a hurry to finish, and when we are done she will be better than new. Probabbly better than most of the $30,000 dollar ski boats on our lakes today, but she'll be in our garage at least another year if not longer. Again we're in no hurry. We made that mistake when we bought her needing a complete redo. Oh yeah and she cost us $3000.00 right up front.
Now after all that I will close saying this is the BEST place on the web to get the help you need for anything boating. There is a wealth of knowledge here and a group of men and women who love boating and love helping fellow boaters. You are farther ahead than most of us by asking the important questions before you get a boat. Most of us found this site after we had picked up our boats and realized we were in over our heads. That Glastron is certainly interesting, and may be a worthy boat to pick up and fix up. If you decide to get her the people here will gladly help you with your questions.
Make sure you take a boating safety course when you do get a boat.
Good luck and keep us posted.