Li-Ion powered Nano & recharge

Hi there, I've been considering for long to start working on such a hard project , which is to build a "smartwatch" like controller. I have some led strips in my room, connected with an NRF24 that I use to turn them on and off... I also dispose of a SPI OLED ssd1306 and some old nokia batteries. The idea is to build an all in one digital watch and remote controller for the led strips (and maybe other future projects). The first problem is for sure the miniaturization, but what I'm intrested in now is the powering system.

I know that the Nano can easily be powered through a 3.7 Li-Ion battery (the nokia one), directly connected to gnd and the 5V pin. I wonder, since the cell batteries do have a protection circuit, if it is almost safe to charge that battery connecting the Nano to an USB port, which would generate a 5V tension on the battery.

The second problem is that the two libraries (NRF24 and the one for the OLED) are quite heavy, and the use around the 75% of the memory on the Nano. But I think I can manage to reduce the size of the sketch, by "cutting" some unused parts of the Adafruit library and by programming directly via ISP, cancelling the bootloader. Thank you!

Overcharging the battery breaks it too. It doesn't like being charged to more than 4.1-4.2V.

A 16MHz nano expects 5V, the battery may drop to 3V or lower before the assumed protection interrupts it entirely, such low voltage could make the nano unpredictable.