If they are not same or simlar cells, how we can get soecific immunological memory or specific antibodies from vaccines as we get from natural infection? If they are non specific then how they will be effective to same vitus?
Antibodies recognize proteins, not cells. Antibodies cannot easily get inside cells. So to help out, cells have these structures called MHC's (major histocompatibility complexes) that present internal peptides to the world outside the cell.
Antibodies drift by these structures. Do they see only autologous peptides? (i.e. parts of proteins normally expressed by cells) Then they pass them by and ignore them. Do they see peptides from viral protein synthesis? Then they attack that cell and destroy it, because a virus is using it to replicate.
So in the future, antibodies will not look at a cell and say "hey, that cell has been infected before.) All they do is look at the MHC. If it contains those fragments of the spike protein, it attacks the cell*. If it does NOT see the fragments, it leaves it alone.
(* Note that antibodies alone do not finish off the cell. Generally they signal one of the many killer leukocytes, like killer T-cells, to get involved.)
Shoud we not need to get more infection expression from vaccines to get more robust immune response than natural infection? One dose is also only advised in some vaccine.
Correct. And they both work in _slightly_ different ways. In mRNA vaccines, there is nothing to recognize and attack until cells start expressing that protein, because your immune system completely ignores the slightly modified RNA. (It does not see it as RNA due to a clever replacement of one base pair.) However, in adenovirus based vaccines, the immune system _can_ recognize the free viruses, and that contributes to the response.
The reason we know they work is not that we decided that they do based on any of the above. The reason we know they work is they have been tested, and they do indeed prevent serious illness ~95% of the time.
Long term antibodies are needed to for secondary immune response.
Nope. You can have zero antibodies (IgM) for a given antigen and still mount a robust secondary immune response due to the action of memory B cells. Of course, a non-zero number of antibodies will speed up the response significantly.
It is worth noting that there are several different kinds of antibodies. The ones most people are familiar with are the IgM antibodies; in an illustration showing antibodies attacking a virus, they are generally showing IgM antibodies. They are large and complex and very specific, and are thus a little more fragile.
IgG antibodies are smaller and much longer lived. They are not created until well into the immune response and are not as specific - but they do last longer.
So if you get reinfected immediately, IgM antibodies go to work right away.
If you get reinfected a while later (say 2 years) IgG antibodies provide some initial defense until the memory B cells start producing more antibodies.
If you get reinfected decades later, then your memory B cells have to produce antibodies before the secondary response gets going.
All of which is why you are most protected right after either vaccination or getting over an infection.
4. One more question to my last post. Can infection/entry of changed genome to cells lead to creation of changed or new type variant vituses?
Again, since mRNA vaccines do not change the genome of the cell - no, it cannot.
HOWEVER, frequent use of any mitigation in a population where the disease is endemic can indeed lead to resistance. This is most commonly seen in antibiotics, but can also occur with vaccines. That's why it's essential to finish the entire course of antibiotics, so you can wipe out all the bacteria and not leave any to evolve resistance. That's also why it's critical to get Re below 1 quickly, to wipe out the virus quickly rather than leave large pools of infection to evolve resistance.