some questions for motorcycle experts out there,

- 3rd new battery in a year - is this alternator problem?, if so how can i test it ? is traveling 10km (x2) a day not enough to recharge the batt or its just because of the cold season.?

- black liquid leaking under the engine, but the engine still sounds and run good... do i need to check something like the gasket, mechanic say its nothing worry with when it stops working then he will check?

- liquid cooler (blue color) leaking on the pipe connection to the engine, is this something to be worried for?

Thanks.