I am a flooring contractor from N.CA and have been so for 28 yrs. I've seen and worked on plenty of those older fir floors. Here is my take on your floor.
It is a combination of subfloor and finished floor. This was a common building practice. In homes of the "well to do", they often would install elaborate oak floors over those fir subfloors in the formal areas on the home. In secondary bedrooms and service areas, they would often just stain, shellac and wax the fir flooring. Or paint it. Sometimes they were left unfinished and large area rugs were placed over these floors. In farm houses, these floors usually were just painted or varnished and area rugs were placed in the formal rooms. So, these are original to the home and are considered the subfloors.
Now, one of the reasons for the gaps is that they were probably always there somewhat. Oftentimes, these floors were hand nailed with regular #8 box head or common nails. This prevented the T&G from fully engaging and closing up. Then, along with foundations of minimal stability and many years of expansion and contraction, gaps have formed. I can pretty much guarantee this is the typical douglas fir subfloor installed in many thousands of residences on the west coast of the US for many years.
But to your questions:
I do not think you will be able to successfully remove this floor without tongue breakage. Plus, it does run under the walls. Since it is a subfloor, from a structural point of view, this would not be a good idea. If you want to attempt to salvage this floor, it will need to be re-nailed to the joists by face nailing and then filling the nail holes with putty. The gaps can be filled with a filler, such as Timbermate, which claims it won't pop out. Then the flooring can be sanded and finished. I did this EXACT thing to a historic home in Martinez. It turned out fine, IMO.
If you want to install another floor, you have MANY options. Unless there is a height issue/problem, I would go over your existing fir subfloor with a new floor, after the fir subfloor was refastened with screws. I would strongly consider sheeting the fir flooring with 3/8" (minimum) plywood to add stability to it. This would allow you to install pretty much ANY wood floor over it. There are many fine engineered and solid wood products to choose from, either factory pre-finished or have it sanded and finished in place. The radiant will potentially pose a problem for solid wood floors. So if you chose to go that route, then make sure you use a stable wood species. If you MUST have an historic looking floor AND it must be installed over the floor joists AND you do plan on removing the existing fir flooring, then I would recommend using a medium width plank floor from Carlisle:
http://www.wideplankflooring.com/ They are not cheap but their floors are the best of their kind, IMO. You could glue and blind nail a 6" or 8" plank floor over your floor joists and have a very nice floor. They are pre-sanded but need to be finished. They have many species to choose from. It really depends on your budget and what you are trying to accomplish. If you are in my business work area, I would be happy to come take a look and provide you with some options. You can reach me at: (925) 778-4844 or PM me on this forum.
Gary Clontz