In the last couple of questions, I observed answers are coming but they cannot solve my problem. Suppose after a long time, I get the correct answer and post it as a correct answer to my question and accept(In case of the last questions, this actually happened). Is it a bad sign to my questions? Or it proves people do not give enough time to others' questions(Needless to say, they were pretty big in size)?
No it has no bearing whatsoever on whether your question is a good one or a bad one, it merely shows that you found the answer yourself.
It proves nothing of the kind. People on SO are generally falling over each other to answer questions.
Answering your own question shows that you have continued researching and trying after asking for help. That is definitely to be encouraged.
You offer two negative options to what self answering indicates, but it is a positive thing to do. I'm surprised it doesn't happen more often.
No, this is actually encouraged. We even have a badge for it, if the answer gets enough upvotes (3 or more): Self-Learner.