Actually, that is a really good project with which to learn stripping/sanding/staining/finishing. It will be much less messy and safer to walls/floors/carpets if the mantel can be moved outside---or into a garage/basement with a concrete floor. Stripping can be done with non-toxic stripper---the orange stuff and a stiff bristle brush. Apply a liberal coat of the stripper and wrap the whole thing in plastic---a painters plastic drop will do nicely. Wear goggles that completely cover your eyes---not just safety glasses---and rubber gloves. Follow the instructions on the stripper container. Getting the stripper off is done with a putty knife---or whatever flat tool works. A second application of stripper may be necessary and than a third which is scrubbed off with the brush to get paint in the pores of the wood. Sanding depende on how the wood looks after stripping and what kind of surface you want for staining. A random orbit sander(ROS) with hook and loop paper mounting will be the best sanding tool. Ryobi makes an inespensive ROS and you can buy packs of 5 sanding discs. You will need 80 grit to start, 100 grit for the second sanding, and 150 grit for final prestain sanding. Sanding with finer that 150 often closes the pores in wood and stain does not work as well. Once you get the surface you want, simply use an oil based stain of your choice---Minwax makes a wide variety---and wipe it on with a lint free rag---wiping off the excess to get the color tone you want---the longer the time between applting and wiping excess darkens the color. Let the stain dry for a day or so and wipe with a rag dampened with paint thinner. Then apply a coat of varnish---a Purdy brush(about $15-$20) or equivalent will let you apply a professional looking finish with just a little practice. Varnish is the most easy to repair--poly is quite difficult to fix mistakes or bad spots. Let the varnish dry for a day, sand lightly by hand with 220 grit paper or 000 steel wool---just to knock off nubbies. Wipe with the thinner rag and apply another coat of varnish. A third coat and you are done.

From the photo you posted it is impossible to see proportions. Post another photo taken full front, showing floor and ceiling. Lacking that, install the mantle at the approximate point shown in the photo above where there is a change in materials. Unless you don't like that point. Then install it somewhere else...good luck!

If they are not structural, get rid of them, but consider that there will be a mark on the floor from where they were. (My parents had to stain match the area on their floors when they removed columns.) I would not replace them with anything. You have too much going on in the space and less is more.

There are some products out there that add patina. Then there is always the old dissolved steel wool trick. None of them look quite like the real thing. If you want a real "weathered" look the best ways to take that thing out in the backyard and let it sit for a year in the weather. Also, finding a weathered beam is just not that hard or expensive. If you want one that is weathered NOW just go get one.