Hi, Im very new to Lipos, and I have a question. Can I charge through the wire I circled in Red in the picture? (The black/red wire that outputs into the aircraft)

Yes you can charge the pack through the thicker discharge wires. Use the proper cell count (if it isn't an auto-detect charger) and charge at a 1C rate (or less) which is 1 times the capacity of the pack. (e.g. 2100mAh will be charged at 2.1amps or less , a 1320mAh pack will be charged at 1.3amps or less)

The other connector is ONLY to balance the pack using TP's cell ballancer, do not try to charge with it.