Is it an FAA certification requirement that aileron can maintain control with flap assymetry?
No, that is not a requirement, and few certified planes I have flown would be able to do this at all, much less within the pilot's strength and endurance.
Yes, all certified planes have demonstrated a "balked landing climb", which will be full flaps, full power, and a decent climb rate. If you must climb away with full flaps out, allow for a shallow climb, and have no fear, the plane will do it. If you have an engine failure doing this, it's going to get scary fast, so do retract the flaps at the earliest suitable opportunity.
The Cessna singles flap system is very robust in terms of asymmetry. The only real risks are those of a pushrod, or track failure. Yes, a pushrod failure could see a sudden retraction, and your only action would be to fully retract the remaining flap. You'd want to have some altitude, and be comfortable in unusual attitudes. I have never heard of a Cessna flap pushrod failure. I have had a broken flap track. There was no asymmetry, the flaps just jammed at 20, and would not retract. I was doing a water touch and go in a Cessna 180, so I was not going to stay, I flew the go, found I could not retract the flaps, decided to not fiddle with them at all, and flew it home that way. The right flap was hanging awkwardly as I taxiied in. When doing your walk around, with the flaps fully extended, do have a look at the track attachments for anything odd. In a Cessna, I am not alarmed by selection of flaps in a turn.
Certain Piper twins are reputed risky for flap asymmetry (I've been warned flying Navajo and Twin Comanche, perhaps there are other models). This is because one flap is driven, which then drives the other flap. The interconnecting drive can fail. So, on those types, small extensions at a time, and if asymmetry develops, easy does it trying to correct things - no further extension, and caution about large selections.
As for a nuisance lateral imbalance, fuel may become the greater annoyance, so have an understanding and plan for that. I was once right seat in a Piper Cheyenne, and a fueling error gave us a 400 pound imbalance at the tip - that was a problem!