Do runway markings vary from country to country?
Do runway markings vary from country to country?

Yes, examples are touchdown zone markings and runway number sizes.

How much do the runway markings vary from USA to Europe?

Europe is too big to manually check each country, but it doesn't vary by much. Numbers are still numbers and TDZ markings still follow the same pattern.

Even smaller airports, say in the US, don't necessarily match bigger airports.

Difference are submitted to ICAO to be included in supplements to Annex 14 when it comes to international airports (typically). And each country's AIP will list the differences from ICAO Annex 14. So if you are interested in a certain country, check its AIP. If interested in the recommended standards, check Annex 14.