Adam and Eve where the very first people on earth. In Genesis, when Cain
is sent away to Nod, it says he takes a wife and she bore him children.
Where did she come from , if Eve was the only female on earth at the time?

Cain would have had to have married his sister. This was not uncommon in the early years of Bible history. In fact Sarah; Abraham's wife was his half sister. Nothing is said about Adam and Eve having a daughter but that is not unusual either as women were not commonly mentioned in the scriptures especially the Old Testament unless they proved to be persons of importance. 

How are we to believe that all mankind started from Adam and Eve?

You can believe that all of mankind descended from Adam and Eve the same way
you can believe anything else recorded in the scriptures. It is not trouble
at all for me to believe it because I believe the Bible is God's inspired
Word. Now down to the practical side of the matter. For thousands of years
following the creation mankind lived hundreds of years and begat children.
We have no idea how many children Adam begat for the scripture says, "And
the days of Adam after he had begotten Seth were eight hundred years: and he
begat sons and daughters. 

We note also that they began to practice polygamy
and a man living for hundreds of years could produce multitudes of progeny.
So I see no problem in all of mankind descending from Adam and Eve. You may
wonders as have many others where Cain got his wife. Evidently he married
his sister and that was not unusual either. Abraham's wife was his
half-sister so it was not uncommon for close relatives at one time to marry.
At that time man had not developed the multitudes of physical weaknesses and
diseases so there were no ill effects from such marriages.

1. If there was only Adam and Eve at the beginning, how did the population
grow without there being any incest?

2. Where did the dinosaur fossils come from if the earth wasn't in
existence when the dinosaurs were supposedly walking the earth?

In regard to the populating of the earth brother had to marry sister for a
short while in fact even several generations of men Abraham's wife Sara was
his half sister. There was no problem with close kin marrying at the time
because disease had not begun to be a problem.

As to the age of the earth no one knows how old it is. Believing in divine
creation I believe all life was created full grown because the natural law
of reproduction was stated following creation that everything would bring
forth after its kind. Immature animal life does not reproduce that is
reserve for the mature of the species. Man was created full grown, now how
old was he at the time? At one day old he was grown. The minerals and all
that composes the earth could have the appearance of being thousands or even
millions of years old when God created it. Dinosaurs most assuredly were
created by God and there will never be an absolute way of determining the
age of the earth when they existed short of eternity itself. At that time
all the secret things will be revealed by God.

What happened to Adam and Eve?

Adam and Eve apparently died natural deaths. As to their eternal
destination that is a matter that only God knows.

Why is so little information given about Eve, the Mother of all Living

We have no idea why so little is given about her or others of hers and
Adam's immediate descendants. Apparently God gave us all that we need to
know about her and we will just have to wait until eternity to learn why so
little is said about her.

Where did the wives of the sons of Adam and Eve come from?

They apparently married their sisters. That was no problem health wise as it would be today since disease and physical & mental diseases had not invaded the human domain so much at that time. Even Abraham was married to his half sister (Sarah).