Can I also just charge through the wall socket?
Not all outlets can handle the high wattages needed to charge your electric car. You should therefore use the outlet only in emergency situations. To be sure, check whether the outlet is getting hot. If so, stop charging. Another thing to watch out for: there are specific requirements you must meet to run a power line across the pavement. Are you able to install a charging station at home? Then that is the best advice.