To answer your first question, as long as your circuit uses less than the 280mA, your circuit will be able to operate while it is charging, but take note that the more milliamps your circuit draws, the longer it will take to charge the battery. For the second question, most lithium ion batteries should be allowed to discharge to about 3.3 volts. You can discharge them to 3.0 volts, but they will have a shorter lifetime. Also keep in mind that when lithium batteries are fully charged, they are at 4.1 - 4.3 volts, which could be a problem if your attiny84 is running on 3.3 volts.