All brake fluid is synthetic. Some manufacturers use that as a marketing tool. Its all glycol-ether based except for Dot 5 which is silicone based and not compatible.
DOT 3, DOT 4 and DOT 5.1 will all mix with each other. Dot 5 will not mix with the others.
Kymco recommends Dot 4. Any name brand will do. One of my favorites is Castrol GT LMA dot 4. Have been using it for over 30 years with no issues.
As for gear oil, I'm using castrol C Hypoy 80 W 90 gear oil. It says on the bottle maximum gear protection for motorcycle, ATV, and scooter transmissions.
I think on my next gear oil change I am going to a 75 W 90 synthetic. Any name brand will do.