What kind of eye protect is appropriate for glass fibre insulation but won’t fog up

If it is in a frame 1/4" glass will be sufficient. Your options for glass will be tempered glass or laminated glass because of it's proximity to the ground.

Tempered glass will break into very small pieces like a car window for a door. Tempered glass is stronger than normal glass.

Laminated glass will break like a car windshield. It breaks normally but it is two pieces bonded together with a plastic. The plastic prevents most injuries as well as the mess from breaking. Laminated glass is more often used for safety/security applications.

Although 1/4" is suitable for the application, I myself am always weary installing it as an interior partition. My family business has built all glass offices in buildings and we use 3/8" tempered glass. 3/8" Tempered is extremely difficult to break. When you get up to thicknesses that large as far as cost goes the difference between 3/8" and 1/2" thick glass isn't very significant.

If you go with a thicker size be sure that your trim is strong enough to withstand an impact of the weight of the glass, the weight of a person, and the velocity they are traveling. This is due to the fact that it is more likely to break from breaking out of its frame and falling down, especially in wood.

If the beams are not structural I would recommend you use a router to create a slot in each beam deep enough to slide the glass in far enough to place it where it needs to go and then slide it back towards the other beam into the slot you created there. This is commonly done with metal storefronts and is called a flush glaze.

If the electricity has been turned off, and you have confirmed it's off via a non-contact tester, multi-meter, or some other method, then you don't need gloves to protect yourself from electrocution - there should be no risk if you've actually confirmed it's off. I even go as far as to put a piece of tape over the breaker so someone doesn't walk by and flip it back on.

I sometimes wear gloves to protect my hands from scrapes and cuts - any work glove you find comfortable for the job should work.

As DA01 said in a comment, a glove that would protect you from shock would likely make working with the wire/cable we find in residential difficult. They do however make insulated tools which can be used when working on live gear. Best to just turn the power off and not worry.