I was wondering if Stack-Exchange will allow me to access my questions at any point in the future even if I end up asking huge number of questions as I go along? Or is it the case that the site can only allot a finite memory to each user and the older questions get deleted? It would be nice to have the all the questions for back up incase I need to look up the answer again. Thanks in advance.
end up asking huge number of questions
You can ask no more than 50 questions in any 30-day period (and no more than 6 questions in any 24-hour period), so plan accordingly.
If you find $50\cdot 12 = 600$ good questions to ask every year, more power to you... But if they are bad questions, they are likely to get deleted even if you have only a few of them. The point is: if you want your questions to stay around for a long time, focus on their quality, not quantity.
Your question are recorded as long as they do not get deleted by votes of other users or a process to clean up badly received content (thanks to quid for making the point more clear). And even then, once you'll have more than 10k reputation you will be able to still see them (after deletion). However, you will not to be able access them so easily as the other which are listed in your profile under question (see here).
There is not a limit on the amount of memory each user's posts can take up.* Stack Exchange can (and does) store all the questions you post, and does not delete old questions to free up space.
It is possible that some of your questions can be deleted, so if you really want to keep a record of them, make copies before you submit them here. But the reason for deletion will not have anything to do with age.
*OK, technically there is a limit, but it's not physically possible for you to write that many questions in your lifetime.