It is limited in that sense, but not enough so you can't have 3 alarms for the days you want to wake up to (I'm assuming that if daily and workdays is out, you're likely to have less than 5 days, thus 5 alarms). If you have a more complex schedule, there are apps out there that allow better alarm manipulation.

Which charging light? The one near the USB? Mine is obscured by the cable. Or is it the "breathing" button light? I think the latter is off while charging if off in settings. If it's the one near the USB, use a bigger cable, my is useless (obscured) unless using one of those thin wall chargers.