What does it mean if a professor does not answer your email in time?
I wrote him an email to ask quick but important questions, like, when do you want me to start. I didn't get an answer even after a week. And similar things happened before as well.
Some professors are notoriously bad in answering emails. This does not necessarily mean anything. Don't fret about it.
So I want to ask that as a professor, sometimes will you (on purpose) to NOT answer emails in time?
I'm not a professor, but, no, this is not how I would expect an adult person (in a management position, none the less) to behave. If the professor is indeed having second thoughts about you and decided to just not answer anymore, I would say you dodged a bullet there.
However, I really think that this is unlikely. Just send a polite reminder, or propose to have a quick chat e.g., over Skype, at a time of the professor's convenience.
Unlike other professionals, academic faculty have multiple competing tasks of wildly varying natures and deadlines. Broadly divided, we need to balance:
Teaching: Two to four courses a semester with dozens, scores, or hundreds of students; a handful of TFs; and occasional irate deans and parents. One or two or three independent readings with students outside of that. Letters of recommendation. Trying to find internships and grad programs for advisees. Handling postdoc requests. Working with academic review committees. Working with course of study committees. etc. etc.
Service: Serving on several unrelated college or university committees. Serving on the steering committees of affiliated programs at the university. Having the provost scout you out for a pet committee. Running a search committee. Doing grad admissions. And this is just university service. If you do service work on your national association, then there is considerable committee work there. Not to mention doing peer reviews of journal articles, book manuscripts, grant proposals, etc. etc.
Research: And if you can find time after all that, there is your own research. Trying to keep several articles in the pipeline, tracking down an editor to listen to your book proposal, getting around to writing the conference paper you promised, etc. etc.
The way some faculty handle the multitasking is by singletasking. They only do postdoc intake work on Friday mornings, for example. Others give up and have a mailbox from hell.
In other words, things can easily get lost. While a simple questions such as yours might seem to be simple, it might require the prof to have to e-mail the department chair (who is even more busy than the average prof) for an answer, which then gets lost again.
I'd give it a week and then politely ask again. Use the same e-mail title (or reply-all to your own e-mail) so as to bump the e-mail thread back up to the top of the prof's e-mail queue. It's important to try to keep e-mail threads together as faculty have limited brain resources and we rely on our e-mail as our offline memory extension.
Since it has been a week, I think it would be acceptable to email them again just saying that you just want to make sure that they did get your email and that you would appreciate their opinion/response/whatever regarding your questions.
Professors receive tons of emails daily, and it isn't uncommon for them to miss important ones that get buried in their email.