This isn’t something the states retained for themselves. The 2nd Amendment’s “Shall not be infringed” is quite clear.
Sure it is. If a state decides they don't want people carrying firearms in courthouses or jails or schools or sporting events then they have the power to prohibit it under the 10th Amendment. If they want to ban felons from owning firearms then they have the power to do so under the 10th Amendment. If they want to become Constitutional carry or if they want to require training to get a concealed carry permit then they have the power to do so under the 10th Amendment. The Heller decision said that states cannot prohibit a citizen from keeping a firearm in their own home. But the same decision said that reasonable restrictions are within the state's power to enact. Under the 10th Amendment.