Are bayonets still used/issued in the modern military?

Yes they are

Yes, but very actively. Many models of the standard issue M- fighting knife still have the loop so that a troop may attach it to his rifle. Also, many drill platoons still use them. For example, Marines of the USMC Silent Drill Platoon use M1 Garand rifles with bayonets.

As an Air Force member, I can state that we do have bayonets in our S-4 (Supply) shop but none of them are issued to any members of our squadron. They sit there and collect dust. We really have no reason to use them in conjunction with our M-4 assault rifles. In today’s day and age, you are going to see virtually no close quarters fighting where a bayonet would be of any use whatsoever.

yes, in my time in the army, we learned to use bayonetts, pretty nasty stuff those can do…
Offcource my A3G3 with .762 ammo is pretty nasty even without its butterknife…