
ANSWER: Your chair probably dates to sometime in the early 20th century. I'm sorry I can't be more exact. It looks like it had been painted and someone tried to strip off the paint. They probably found it too much of a job, so they just abandoned it.
You’ve probably heard on the Antiques Roadshow that refinishing antique furniture can diminish its value. But in a case like yours, it can only improve it.
I would suggest fixing the chair. The part that seems to be apart on the left side of the seat can probably be pressed down and reglued. Use a generous amount of Elmer's wood glue and several C clamps. Let it set for several days.
After the chair dries, you'll want to sand it---first with a 150-grit sandpaper wrapped around a block of wood or one of those sanding blocks. Follow this with a finer grade.

one-coat paints, in this instance you probably should use an undercoat and a final coat. The wood is dry and has been through a lot, so you'll want to seal it. Frankly, you can paint it whatever color you like. If you can see the color of the old paint, you could use that as a guide. Choose a semi-gloss finish. And give the seat at least two coats.
Even if a piece isn’t a rare antique, it’s best to take the path of least resistance. Sometimes, all a piece will need is a good cleaning. Murphy’s Oil Soap will do a good job while giving the wood back some of its much-needed oil.
If you have a piece of furniture with parts missing, you can try to replace them. However, this may take more woodworking skills than you possess. The best advice is not to try gerry-rigging a part if you can’t find a replacement and just leave the piece as is. Finer pieces may indeed be worth the cost of professional restoration.
If you can fix up this old rocking chair, it will make a fine addition to your porch and give you pleasure for years to come.
To read more articles on antiques, please visit the Antiques Article section of my site. And to stay up to the minute on antiques and collectibles, please join the other 18,000 readers by following my free online magazine, #TheAntiquesAlmanac. Learn more about the Victorians in the Winter 2018 Edition, "All Things Victorian," online now.