I am a 30 year old male citizen of Singapore. Previously I studied at Northwestern University for 7 years from 2004 to 2011 , but due to poor academics , dropped out of school 3 times. The last time I reapplied back, I got a visa refusal under section 214(b). After that, I went back to Singapore and applied to Monash University on Australia and got accepted --/ I went over to study but after a couple of weeks , dropped out and returned to Singapore and cancelled my student visa. However on my Monash university application form , I did not declare that I was previously denied a visa. And on the Australian visa application form , under " Have you ever been refused entry to any country on character grounds " , I wrote no because I thought character grounds meant criminal record. I wasn't caught but I am really worried it will come back to haunt me when I apply to become a citizen of another country ( an option I am very keen in ). Any ideas what I should do ?
TL;DR: You're fine.
Making a false declaration to an immigration authority is a big deal and can back to haunt you if you are caught. However, "character grounds" refers to have a criminal record, which you do not have. So you have not lied to the Australian government.
Making a false declaration to a university can get you expelled from that university, but will have no impact on anything else. (Also, since you did get the visa, I don't see how the university could possibly ever find out that you had previously been denied one.)
In general, the immigration authorities of various countries do not cooperate at all; getting them to exchange information even when you want them to can be really painful. (Here's my own little story of how hard it was to get the Singaporean police to talk to Australian immigration.) So unless you end up on a multinational terrorist watch list or have an Interpol arrest warrant out, it's really unlikely that the Bulgarian authorities would ever find out (or, frankly, even care) about a US visa refusal.
All that said, it's still the best to tell the truth whenever you possibly can when dealing with Immigration. They're trained to sniff out inconsistencies and lies, and as stated getting busted is really bad, while honestly explaining a story that doesn't involve any crime or other real misbehaviour on your part is not a big deal.
Well I just called an agent from the study abroad office in Singapore, and she said it won't matter because " character grounds " meant something serious like a criminal offence, whereas I was rejected a visa for academic reasons ... Still , on the university application form itself I said no to the question " have you ever been refused a visa "