Is there any kind of quota on how many or who can obtain Nationalization to become USA Citizens?

Any "quota" would have been fulfilled at the time they were granted their green cards. There are caps on how many can legally immigrate to the US each year and that to some degree controls how many would be eligible for naturalization three, five or more years later. The population control element occurs much earlier in the process.

No. There is no quota on naturalization. Anyone who qualifies can apply and naturalize. There is only a quota on certain classes of people getting green cards. There is no quota on certain other people getting green cards. So in reality, even green cards are unlimited.

No, people who qualify can naturalise

There are required qualifications to immigrate to the US & obtain legal permanent resident status. There are numerical limits on the number of immigration visas issued each year, with specified limits for each subcategory of immigration. E.g. see the monthly Visa Bulletin for Priority Dates with visa limits for, say, those with sibling petitioners, or adult children of citizens, etc.

For legal permanent residents (green card holders), there are also specified qualifications before one might apply for naturalization. E.g. the legal permanent resident must have actually resided in the US for a minimum of 5 years from date of green issuance, or 3 years if green card obtained through marriage, to be eligible for naturalization. There are additional requirements besides actually residing in the US. There is no numerical limits on naturalization, if the legal permanent resident meets all the required qualifications.

There are four ways to become a US Permanent Resident:

1. Family sponsorship. There are quotas on how many visas are issued for parents, adult children, and siblings, but not spouses & minor children.

2. Employment. One must be on an H1B work visa for six years before their employer can sponsor them for PR status. There is a limit on how many H1B visas are issued each year.

3. Investment. It basically requires US$1 Million invested in a company that will create at least 10 permanent jobs. I don't think there is a quota for investment visas.

4. Be in the USA as an asylum seeker or refugee whose petition for asylum or refuge has been approved. No quota.

Once someone has been a US Permanent Resident for five years they can apply for citizenship (three years if married to a US citizen). No quota.