After training pull-ups, chin-ups and dips for a while I started adding weights(slowly with the same amount of set and reps). My weight is ~86kg and I currently add ~12kg using backpack, and do 5 sets of pull-ups or chin-ups (15, 14, 13, 12, 11) and 5 sets of dips (12reps) in 1 training session.
I know that if my goal were building muscles I would better add more weight and make less reps. But is it healthy to suddenly add more weight and isn't it harmful for spine?
If it's harmful for the spine, it will let you know in the form of pain or exhaustion.
Since you're working with weights less than 100kg, there generally isn't much reason to believe that your back can't handle it. Adding 12kg to 86kg isn't a drastic change. Your skeleton has already handled weight on this order for a long time already.
If you're able to do the reps, it's safe to say your back is up to the task.
I assume here, that you're not going from bodyweight to adding weight in huge increments.
To build muscle, it is best to do a variety of repetitions. There is no magic number at which your spine will be hurting (especially as biomechanics do not cause an injury). Try to do one session a week with heavier resistance and repetitions of 4-8, and on the other session with repetition from 8-12 or higher as you do now. This way you will build more volume more frequently hitting different muscle fibres.
