Not exactly. If you use the same soul as your last character what you retain is skill ramps, this allows you to reach the same level you were before much quicker. In turn that allows you to actually become more powerful in the next life. You will not necessarily start from zero skill either as your character will have learnt skills during their childhood based of their parents and region.

So no, you do not just keep the same skill level, but your previous life dramatically impacts your skills this life and allows you to continue to advance.

Yes, and it would make a difference. Hypothetically, let's say you reach 60% mastery in a single life. Starting over with a new character, you could now reach 75% in the next life. However, if you already trained your heir up to 20%, you might now reach 80-85%.

Note that all these numbers only serve to illustrate my point, there is no concrete information available at this point aside from the knowledge that it will make a difference.

You would still have a skill ramp but it might not be as high as it was.

One thing to point out is that with each passing life, the skills you gained in your first, second, third, etc… life will have less and less impact. However, if you continue to develop those skills with each successive life, the benefits will be compounded.

[Source]

We do not have firm numbers but it might well be that if you ignore that skill you had got to 60 for a life when you next go to increase it you find that you only have a skill ramp to 40. So still some benefit if you return to it soon enough but not the full effect.

Yes, but it will be smaller than it was in the second life. You will keep some of it, but unless you train it in your current life it will diminish.

Edit: Seems like I wasn't fast enough -_-

say you have s school and in this school,like a university or collage.you want to teach several skills.will thios be posable and if its youe school what will be your benefit?