Thank you for your fast answer and for your golden advices! And sorry for my bad English!
You're welcome. And don't worry, you're doing fine.
1) Do you suggest me to peel the brown outer skin or it's better to let the nature do its job?
I've found that it's better to peel it off. Typically, the skin is softened where the seed is underwater, but tends to cause the water to spoil faster, and it gets dried and often prevents the seed from splitting, which it needs to do for the sprout to grow. If the skin is difficult to remove, pick at it with your fingernail from the base of the seed and peel a little at a time.
2) I'm really "on an empty stomach" with gardening, sorry! When you say "sand", you mean the sand of the seaside?
Although you can use the seaside sand, it's vital that you wash the sand thoroughly to remove any salt. (For all gardening projects, but avocado is particularly sensitive to salt.) It's better if you can get a freshwater riverbed sand.
I don't know what kind of shops you have there but sand sold for underlaying brick or stone paver projects are usually suitable for potting soil as well. Be careful though, they sometimes use "granite dust" which is generally alkaline -- not suitable for avocado.
Ideally, you want "sharp" sand which is well-draining, not sand with rounded edges, though I have to tell you that I regularly raid my children's sandbox, which is filled with "Play Sand" -- sold here in bags after being thoroughly screened and washed or sterilized. This is "soft" sand -- with rounded edges.
3) I discovered that from the seed of avocado grow different roots: from the "base" of the seed and sideways...on youtube I have seen a cultivatur cutting the roots grown from sideway. Is it right? What's the possible reason why?
This is very interesting. Only reason I can think of is that these roots would eventually grow into shoots, and they plan to graft a known variety of avocado onto the seedling. This is the usual practice for getting exactly the kind of fruit tree desired. The seedling is called "root stock" and is not considered important. There is a varying amount of advice on this issue, but fruit trees grown from seed are often cross-pollinated by another variety and will not produce the same quality fruits. Also, seed-grown trees will take much longer to mature and start flowering and fruiting (7~9 years or more as opposed to 3~5 years of grafted trees).
Could you post the web address for the youtube video? I would very much like to see it.
4) What are the right dimensions of a pot fit for planting avocado?
For planting a seed, a pot that is 10cm wide and 15cm tall would be sufficient. When the roots start to grow out from the drainage holes, you should repot the plant to a pot that is one or two sizes larger: 15~20cm wide and 20~25cm tall. Young avocado leaves are sensitive to the sun and will get sunburned unless you gradually acclimate it to harsher light. Don't let the soil dry out, but don't let the pot sit in water. Avocado's roots will rot if kept wet all the time. Avocado leaves are sensitive to frost, and the tree itself will die below freezing temperatures.