compact project, powerering and charging

BruceM:
hi every one, I have a few questions about powering and charging my project, I'm using a 3.3v proMini, a 3.7 lithium battery.

I was planning on using a TB4056 for charging protection, it has a mini USB plug and also two pins I can connect other 5vdc supplies to. I was planning on using two 5v 30mA solar panels in parallel to equal 5vdc @ 60mA.

A) is that sufficient to charge the battery? (batt # 503759)

B) I've read that with a 3.7vdc power supply that you don't really need to use a voltage regulator on a 3.3vdc system and the battery can be connected directly to the VCC pin on the proMini
Is this a true statement?? it sounded a bit iffy to me.