Honestly, if you got a fake, or a broken pico, IDK about the cells. I would just return it if you can.
Although I myself am not a fan of picos, well, in the brief time I owned an authentic one, it worked fine, was reliable etc. I wasn't a fan of battery life and the mod generally, but I used Samsung 25s in it, which are my usual battery. But I am a very low wattage vaper.
You should tailor your (authentic) battery to how you vape, not *necessarily* the mod specs, although if you want to vape at higher wattage, you will need a single battery that is rated to perform well. I'm not saying your batteries are good or bad necessarily (although, they should be from a site that is trusted to be authentic and most people use the big three (Sony, Samsung, and LG) depending on what you want to vape it at, will depend on what type of battery you use.
Did you get your battery from a source you know is authentic and etc. ?
This blog is a helpful resource for figuring it out...
Mooch's blog | E-Cigarette Forum
Anna
Anna.