To answer part of the question, and limiting my comments to one specific area, Schengen countries do place stamps in your passport during the application process so that a refusal would be visible to anybody who cares. Furthermore, they share information about visas and visa applications through a database so there would still be a record of any refusal, available to all consular posts of all partner countries (and not only to a single embassy) for some time, even if you immediately renewed your passport.
Legally speaking, a new application would not be automatically refused merely because a previous application – even an application to the very same country, let alone to another one – had been refused but only if it appears that you still do not meet the requirements (there is a separate database for bans, which do legally imply an automatic refusal, but bans are only imposed for serious violations or public policy reasons, not because you failed to meet the visa requirements once).
In principle, even with several refusals on your file, each new application should therefore be evaluated on its own merits but that does not mean consular officers will not look at your history so it's even more important to have a very strong application if you have been refused a visa before and to be especially careful to address all the issue and to highlight what changed in your situation to make you a more reliable applicant.
Of course, if your application is refused (or a visa you already have is cancelled) because you are suspected of fraud, it makes a big difference as your credibility would be seriously damaged. But technically it still isn't necessarily a reason to automatically refuse an application in and of itself. It's just a part of the whole picture consulates take into account to decide whether you are likely to violate the conditions of a new visa.