The Chabad House is located at 10 vakhtang gorgasali 10 Batumi georgia 6010.
No, unfortunately. Global corporations manufacture products with identical names in different places in the world.
Nestle ice cream products sold in Israel are manufactured under kosher supervision. Nestle ice cream products sold in Georgia are manufactured elsewhere in the world, and no kosher supervision agency has ever checked their ingredients
Since we only eat halav yisrael, we have no information about this.
Only Tbilisi has a kosher mikveh, and you'll have to coordinate your visit ahead of time.
Shabbat services are held in Gori and Kutaisi, but they don't always get a minyan.
Many kosher staples can be found in Georgia, and you can have updated list of kosher products e-mailed to you.