I can't speak about the other prophets, but I can talk about Abraham. Basically, we can't know if he existed or not. The 'facts' that we have don't mean that he could not have existed (if we see the story of Abraham being a story continued by oral tradition and therefore having certain details, such as age, exaggerated, and not looking at any of the religious aspects of the story because let's not go there)- but there is no way we can prove anything currently.

What we know from tradition is that Abraham was born in Ur. That to me makes the idea of an Abraham (although not necessarily called Abraham, of course) more likely, Ur was the city of Mesopotamia, it was a port, it was close to the (Persian) Gulf, it had a large population of over 10,000 (large for the time) at the time Abraham was supposed to be born (2100-2000 BC). It was a thriving place and must have been buzzing with life- and unlikely to be as stagnant as many other places. It would have been buzzing with life and ideas, and the traders, from everywhere from modern day Turkey to modern day Egypt to modern day Israel, the large population, everything would add up to create a fertile ground for new ideas- it seems reasonable that someone like Abraham could have been born in that city, at such a time when the city was at its height. Of course, there is some dispute over Abraham's birthplace, and we can never really know.

Haran is of course the place he leaves to follow G-d's word. Haran was also a busy, but much, much smaller place, a smaller trade and commercial centre. There, Abraham would be able to meet people of many different ethnicities, from many different cultures and with differing religious beliefs, as well. Meeting new people with different beliefs and values shapes our ideas and opinions- and this part of the story, of Abraham going to Haran and after going to Haran becoming monotheistic, isn't unbelievable either, in fact, I find it quite believable. The rest of it, I can't say much about how much I find it believable, but Ur and Haran seem the perfect places in Mesopotamia for a completely new belief system to have been created- they are perhaps the obvious places even. If Abraham did exist, then I find it highly likely that the initial parts of the story are true- that he was born in Ur, and moved to Haran.

Of course, we've two questions. 1) Did Abraham as we know him from the Bible exist? 2) Was there ever an Abraham type person?

It stands to reason that there must have been an Abraham type person. Man or woman, old or young, from a different ethnicity, culture or city, someone hit upon the idea of monotheism some 4000 years ago, probably, maybe before, but it just didn't spread or get off the ground. When I talk about 'an' Abraham, it is that person I'm referring to- the first monotheistic person- not the first person to spread their beliefs, or the Abraham as described in the Bible. The first monotheistic person might never have told anyone, hell, they might have been thousands of years before 2100 BC, but if monotheism was going to be founded, then Ur and Haran were ideal places, and that time period, a time with many battles and wars, which would affect your beliefs and opinions greatly, where cities had wide trade links as well, with growing urban populations, seems to be the perfect place for monotheism to be created.

The ages for, eg, Sarah, given in the Bible, are improbable- well, impossible- so we know that can't be true. We do not have any records of Abraham in any of the places he travelled- despite the fact he was a wealthy person, and said to be a military commander at one point. That doesn't mean Biblical Abraham didn't exist, but there is no proof he did either.

To sum it up, I'd say we can't know whether Biblical Abraham existed. We have no proof, no evidence, no contemporary sources to support him ever existing in that time period. But some basic details- such as travelling a lot (at a time with many battles and invasions going on, moving around a lot wasn't uncommon exactly), travelling to the specific places mentioned in the Bible, being born in Ur and going to Haran, aren't unlikely, which supports the idea of the story of Abraham being based- almost certainly very vaguely- on some truth.

Did an Abraham exist? Yes. We have proof in Judaism, Christianity and Islam. There was a first person to be monotheistic, there was a first person to spread their monotheistic beliefs, they could even be the same person. An Abraham type certainly existed. An Abraham who lived nearly two centuries with a wife who gave birth just before she was a hundred years old? We have biological proof that that just isn't possible. We have no archaeological record of Abraham's existence. So I would say, Abraham is not a known historical person, although there is evidence all around us that an Abraham type person existed, as a founder of monotheism, not as described in the Bible.