Q1: When charging the battery via a USB port (100mA and 500mA) and during that time the my system is operative, meaning that several modules in my design can reach 1.2A during transmission, can this by any way case harm to the USB port?
A1) No. The USB input is has a current limit that is programmed by the ISET2 and will "clamp" the input current to 100mA or 500mA. If your system pulls 1.2A it will come from the battery or battery capacitors or the system will crash. Therefore, if your cell is dischraged and you have a large pulse, the battery voltage will drop and possibly the system will crash.
The charger will deliver the programmed current until the timer expires.
If an adaptor is available, you may want to look at a power path part like the bq2403x or bq2407y, where x=0/1/2A/5 & y=2/3/4/5
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