Generally, what is the likelihood of changing US constitution so that a person will be able to run for presidency as many times as she/he likes? I mean in the nearest future, 5-10 years time horizon.
The general odds of any Constitutional Amendment are extremely low. Amending the Constitution is insanely difficult, and the only reason an Amendment abolishing term limits would get rolling would be if there were an extremely popular two term president out there, and
that would guarantee that the entire other party would be militantly opposed to getting rid of the term limits that are the only thing preventing them from getting wiped out in a landslide.