Yes they can. They can even remove deadies using an upper entrance, so a mouse guard is no problem at all.
Not to my knowledge. I just made an entrance reducer with a maximum opening of 9mm tall. An adult mouse skull is 9mm across in the smallest dimension (don’t ask how I know, but yes, I did lab work in neuroscience once…), so as long as you keep the opening at that size or less, you will not get an adult mouse in your hive.
You can make such a reducer very simply by gluing (a good PVA glue is fine) craft sticks or paint stirrers into the right size to wedge into the entrance. If the opening is less than 6mm (1/4") tall, because of stick thickness, sand it so that it is bigger than that to help with trash removal and drone escape in the spring.