Is the -ов surname suffix the most common one in Russia?
I would say yes.
I used the code below to parse the jury pool roster for Khimki district court (the first Google hit for список кандитатов в присяжные with an actual list). It is supposed to be a random selection of the district residents.
curl --silent https://www.admhimki.ru/okrug/prisyazhnye-zasedateli/spiski-prisyazhnyh-zasedatelej-dlya-himkinskogo-gorodskogo-suda-moskovskoj-oblasti/obshij-spisok-kandidatov-v-prisyazhnye/ | pup "table td.xl65:first-child,td.xl67:first-child text{}" | egrep "[оеё]ва?$" | wc -l
Out of 24088 persons on this list, 14415 (~60%) have a surname ending in -ов and its phonetic and gender variations.
This is by no means an unbiased sample (only Russian citizens are included in the list, and from only one region), but I would expect the same or similar distribution of all of the European part of Russia, where most Russians live.
Does the -ов surname suffix in modern Russian mean "a descendant of the person mentioned in the surname"?
The suffix forms a possessive form of a masculine or a neuter noun, similar to English "'s". Its feminine counterpart is -ин, another common ending of Russian surnames. It doesn't unequivocally mean "descendant". You could say это Петин ("that's Petya's") to answer чей это мальчик? ("whose boy is it?"), but you would need context to do that.
Regardinig my second question: from what I've read on the Web, initially a name like "Иванов" meant "the son of Иван" ("Иванов сын", i.e., "сын Ивана"). Later, this name was passed down to the son's son, and then to the son's son's son, etc. Eventually, the name took on a new meaning: "a descendant of Иван" ("Иванов потомок"). Similarly with the other surnames ending in -ов. Is this understanding correct?
That was one pattern of name forming.
As it happens with patterns, it ultimately came to mean "if you want to form a surname from a word, add the gender-appropriate possessive suffix to it".
This pattern was used to form seminary surnames, surnames for non Slavic-speaking peoples of Russia, ad-hoc surnames that people would adopt, etc.
In other words, if you come across a person whose last name is Велосипедов, don't assume one of his ancestors had the Russian word for "bike" as a nickname.
Most probably, he went to a seminary, where he was given this last name by means of slapping the suffix -ов, well known for forming last names, onto the end of a Latin word of the rector's choice.
