Is possible to create a new discussion type that function same like discussions but has it own sets of categories
I suppose it is possible. There is a precedent: the QnA plugin.
In the DBase, the discussions can take a Type
You can set which Categories will have what Type.
And the rest is sheer determination on your part. Start by copying the QnA plugin. Hopefully the bulk of it is not in the vanilla core.
Ha, maybe I can, in the future, make a plugin that allows various discussion types ...
Does anyone encounter the need for this additional discussion type and was able to create a lean working plugin?
There are many things folks have done around here that might match what you are looking for. Could you explain what your goal/needs are?
There is a light plugin that sets markers, but does not go all out to create a discussion type