Which tools should not be operated while wearing gloves

Considering how little exposure you will get to the mortar for your small project, you're probably fine with just your work gloves. Wearing latex gloves under your work gloves will provide additional protection. I would suggest that for the people who will be working directly with the mortar.

Big picture, more important than gloves is breathing protection. Inhaling dry mortar powder can be very dangerous, even in small quantities. Different people have different reactions: while one person could spend years breathing the stuff and never have any problems, another could experience severe respiratory distress on their first exposure. Whoever is opening bags and mixing should be wearing a respirator. The disposable kind is fine, if rated for mortar exposure.

Depends on the voltage you're working with.

If you're working in a residential setting, simply turn off the power and wear any type of glove you find comfortable (including none).

If working in an industrial setting, where turning the power off is not an option. You'll have to choose a glove system based on the voltage you'll be working with. A glove system should always consist of an appropriate insulating glove, and a protective leather glove. A glove liner is an optional part of the system, and can be worn depending on how dainty your hands are.

ASTM D120-14a divides gloves into the following classes:

• Class 00 - Good for up to 500 volts.
• Class 0 - Up to 1,000 volts.
• Class 1 - Up to 7,500 volts.
• Class 2 - Up to 17,000 volts.
• Class 3 - Up to 26,500 volts.
• Class 4 - Up to 36,000 volts.

WARNING: Always properly test your gloves before each use. Visual inspection and air testing is the most common method. If you're using these gloves, you've hopefully been trained how to care for and test them. If not, you probably shouldn't be doing anything that requires you to use them.