Hi there, when teething you really just have to follow their lead and ride it out. Finn shortens his A time and is a right grump, goes off his bottles, a generally unhappy little mite. I just let him dictate when and how long he needs/wants to sleep, within reason. Finn also started teething at 12 weeks and had his first 2 teeth by 20 weeks. He now has 8 teeth at 8.5 mths lol...and is teething again in a big way, so more on the way. It happens earlier and goes faster in some bubs.
With feeding we have often done and do split feeds around naps. Once the teething is over they usually go back to eating their regular way.
In our house it's ok to use a little APOP to get through, rocking, soothing, whatever we need to do at night and for naps. When he's not teething we go straight back to routine and independent sleeping, he's good at making the switch up. I should say that we always try to settle without using APOP BUT we are not afraid to use it if we need to. It depends on how your LO is and how comfortable you are with accidental parenting.