There is no set amount, and you can negotiate whatever you want. In this area in about 90% of transactions, the buyer's broker gets paid roughly 2.5-3% from a coop when working with another broker through the MLS, so they will request a similar amount when working with a FSBO, although in these situations it would be easier to negotiate less.
It may matter whether the buyer discovered it rather than the buyer's agent. However, the buyer may have signed an agreement with the buyer's agent that keeps them involved. If not, no, technically they don't need to cut in the buyer's agent unless they want their agent to represent them. The buyer does benefit from their agent's advice and consultation. Additionally, the buyer's agent has showed them properties, consulted the buyer about the home-buying process, and it just isn't fair to make the buyer's agent work for free. Buyer's agents do a lot of work and oftentimes get nothing in return, and their buyer should be looking out for for them as they look out for the buyer.
Yes, sometimes the buyer will pay, but this is very rare and generally unlikely.
Cut the buyer's agent in and be happy that you may have sold your home.