The charger claims to work with

Any other RC 3.7V 1S LiPo battery with JST

The batteries are Micro JST 1.25, so not sure if the charger will work. I use this one to charge mine

The batteries you linked are the correct ones, yes.

Do you not want to solder or you dont know how? you can build one with an F3 board so you can add beta flight for a little more (if you have a transmitter already that is)

If you fly with 1s batteries a balance charger might not ever be worth it. (You can't balance a 1s battery) I use the IMAX b6ac but I have 2 other quadcopters that run 4s.

It's nice being able to parallel charge 6 batteries at a time, and makes batteries last longer being able to storage charge. Which both likely do. You'd need a paraboard to do more than one Inductrix battery https://www.amazon.com/dp/B01ID6U4LC/ref=cm_sw_r_cp_apa_vpKEybSJESZA6

You'll want more batteries for sure. You'll probably also want a nicer charger so you can store your batteries after use and so you can charge more at once. I've been happy with this charger and a parallel breakout board. Whichever charger you end up with, make sure it says "LiHV" and not just "LiPo" so you get one that supports 4.3v high voltage LiPos and not just the standard 4.2v.

Go ahead and buy some spare props, too. The one thing I don't like about my Tinyhawk II is that the props fly off easily in a crash.