Who are they?
Why did God create them?
Can a mortal become an angel?
In Christianity angels always have male names, but I suppose angels are genderless?
Can angels (other than Lucifer) fall from heaven?
Does each person have a personal guardian angel, and can this angel be seen & spoken with?
There have been several different schools of thought in Judaism on the matter of angels. None have ever been universally accepted as dogmatic, so we are entitled to a certain amount of lattitude on what, precisely, to believe in this regard.
There has certainly never been agreement about why God created angels. Some midrashim seem to indicate that He created them as "first drafts" of humanity; some that He created them in order to help with the creation and maintenance of the universe (for whatever reasons, we do not know, since presumably He could do it all Himself if He wanted to); some that He created them in order to be "go-betweens" between the Heavens and the earth, for such times when it was not feasible or practical for His own presence to manifest; other midrashim speculate other reasons.
The Rabbis of the Talmud indicate that there are several different kinds of angels, some of which are continually being created, praise God for a moment, and then are uncreated; some of which are created specifically for the duration of a certain "mission" or "errand;" and some of which, once created, are eternal (subject to God's wishes). And of those, there are also various kinds, some of which we know of, and have names, and others of which we do not.
Jewish sacred text refers to
serafim ("burning ones," angels associated with some kind of fire),
ofanim ("wheels" or "cycles," possibly angels without humanoid form, or possibly angels that move in a wheeling or cyclical motion, or possibly both),
keruvim ("bearers," or "lifters-up," possibly angels associated with clouds, or imaged as bearing up the Heavenly throne, or having wings), and also
chayot ha-kodesh ("holy beings," angels which are said to be roughly humanoid, but having many wings, and the aspects both of human beings and of other animals); the general term
malachim (usually generically translated as "angels," but actually meaning "emissaries") may be either a blanket category, or it may refer to another subgrouping of angels altogether.
The Rabbis of the Talmud say that everything in the universe has a
sar, which is to say, an angel appointed to oversee its existence. Whether that means that every person also has one is subject to debate.
They also taught that angels (in their natural and true forms and states) do not eat, drink, die, give birth, excrete, or have sex. Some midrashim indicate that angels may sometimes take on aspects of the male gender, but other midrashim indicate that they may also sometimes take on aspects of the female gender. But the tradition overall seems to indicate they are naturally genderless.
We are also taught that angels have no free will. They exist solely to serve God, and have no other purposes or desires. Thus, they cannot rebel against God, since they are incapable of desiring anything but His will (which is why we do not believe in the Christian Lucifer or their story of the fallen angels). Though, in Kabbalah (Jewish mysticism) some of the highest angels are portrayed has being very close to human in some of their words and deeds. The highest angels are the
sarei ha-panim, "the princes of the Presence," who personally minister to God's most complex and potent commands, and are closest to God's Infinite Presence.
Set over the
sarei ha-panim is the chief of the angels, the Metatron: the only angel who was once a human being (as Caladan mentioned, this was Chanoch, the grandfather of Noah, who was transmogrified into the Metatron instead of dying).