In some cities, buses use overhead wires and contact bars for power. (Example from San Francisco.)
Yes, but you don’t have subcompact buses, and giant Canyonero-sized buses, and motorcycle buses…the buses are all the same size, they happen to be almost as big as anything else, so the high wires for them aren’t a problem. If you had a mount a pantograph on a Miata that would hit that wire, well, that’d be a sight 
Eh, a contact bar doesn’t need to be very heavy, so the structure supporting it doesn’t need to be very strong. Some vehicles would need taller contacts than others, to get them all up to the standard wire height, but so what? And of course some vehicles would just skip the contact bar: Fine, then they miss out on the easy power source.
As a former bus rider in San Francisco, I can report that overhead wires are far from fail-proof, and that’s with buses sticking to defined routes. At least once every few rides, the driver had to get out and reposition the contacts.
It will give the A.I. something to do… figure out your optimal route based on battery size/induction charging/overhead charging/plugin charging
If you want to use overhead contact power, you just put the charge line in the center of the road at about 8’ high and designate that as the traffic lane: if you need to pass, use the middle or shoulder lane. In the center, less construction is needed to serve both sides. Of course, with typical traffic volumes, those things would have to be replaced often.
Yes, I remember the few trolley bus routes in Toronto back in the day, and even the streetcars - the driver getting out to reseat the contact onto the overhead line was not unusual, particularly where overhead lines crossed at intersections or at a fork in the road. Batteries are looking better the more we discuss this.
When I plug into a supercharger with my Tesla, it adds a thousand miles per hour of charging for a low charge battery… typical stops are 20 minutes after 4 hours or more of driving. That’s a lot less construction and maintenance than hndreds of miles of overhead line or buried induction cable.
I have a photo somewhere of a bus in Naples - it looks like a short miniature version of a North American bus, center load doors, probably seats about a dozen people. Around here, suburbs are served by the same giant diesel buses that handle downtown, but outside of rush hour rarely have half a dozen people riding. I would imagine computer traffic analysis could size the bus for the anticipated load and use a lot less energy, diesel or battery.
But you’re back to the same problem - charging a fleet of busses would possibly require the same electrical feed as a small subdivision. To some extent, the staggered needs of busses tag-teaming each other could spread the load, but it’s still a big investment.
I would suggest that maybe instead of “charge at each bus stop” there might be a fast charger located at the end of each run, where the bus typically sits for a few minutes to get back on schedule. Charging 5 minutes every so often could probably help. The only downside is that if traffic problems slow the bus, it cannot charge if it wants to stay on schedule - so logically, a bus cannot rely on intermittent recharging; charge at the end of a shift is the most reliable.