What brand is my chain? It has '3f-2' stamped on the plates but I can't tell what the brand is. Thank you.
It doesn't matter. Chains are commodity components made to standard sizes, and the chain you have doesn't seem to be a high-end chain, as it has none of the weight-saving cut-outs that a fancier chain would have.

You need to get a chain that's the same width and has the same number of links. The width is determined by the number of cogs you have on the rear axle (and chains are literally sold as, e.g., a ten-speed chain). You'll need to shorten the new chain to the same length as your current one by breaking links with a chain tool; there are plenty of videos on YouTube that will explain how to do this, or just get your local bike shop to do the work for you.