Some areas can be cleared after 10 or 15 random encounters. In those areas, when you try to rest while encamped you can be interrupted. Do those interruptions count towards the ten random encounters?

It's 15 random encounters. Not only due the interruption encounters count towards the random encounters, but apparently, due to a bug, they start to take the place of the set encounters once the count goes over 15. If you want to have all the set encounters in the slums, as was intended, make sure you don't go over 15 random encounters through rest interruptions. (Of course, if you want to exploit the bug, you could use this to skip the ogre and troll fight in the old rope guild. On the other hand, If you want to challenge yourself and get the experience points I would strongly recommend doing the fight.)

Actually it was the Cadorna Textile house I was in. It is 10 there and in Podol Plaza. But thanks the info helps.