What is the point of the Zaishen Menagerie?

Just a few questions about the menagerie

What is the main purpose for the area?
If I unlock a pet and give it to the tamer, a level 5 version shows up in my menagerie. Can I death level that pet into a level 20?
If so, can I come to my menagerie and tame any level 20 pet that I have unlocked and already trained?

Thanks in advance.

you deathlevel the pets to 20 yes. The whole point ot the menagerie is so rangers and other players that wanted pets could just switch out to other pets instead of destroying their pet they lvld to 20 to cap a lvl 5. Also pvpers can use these pets.

It is just faster to go there and charm a lvl 20 dire/hearty pet instead of capping a lvl 5 and training it all over again.

How can I get the pets in my menagerie to level 20, because I brought in a level 20 reef lurker, but a level 5 one showed up in my menagerie. Do I have to level it inside my menagerie?

Once you've unlocked a pet by showing it to Emryd, you'll see charmable level 5 versions of that pet roaming about in habitats specially designed to meet the pet's needs. To see higher level versions, talk to Wynn in the Training Yard and she'll bring them out.

Read all about it here.

http://guildwars.wikia.com/wiki/Zais...agerie_Grounds

You can also level your pets with Zaishen Coins or Balthazar Faction, as explained on the wiki page that Covah linked.

And of course the other point is that the zaishen menagerie unlocks pets for the whole account.

The main point of the menagerie, as far as I can tell, is to make it so that once you charm a pet on any character, it's available to all your characters and their heroes.
Back in the day, if you wanted a Black Widow Spider as a pet for your Necro's ranger hero, you had to actually take the hero into the Underworld and charm it (like I did). Now you can charm one on any character, put it in the menagerie, and get one for any other character or hero.
It also allows you to change pets without having to go re-charm the hard to get ones. For example, I had a Black Widow on my Ranger once. Before the Menagerie, if I wanted to get one again, I would have had to re-charm one in the UW, but now I can just get the one from the Necro hero, in the Menagerie.

Also, the ability to get specific evolutions to go with specific builds (basically, dire vs. hearty) is nice.

can all the chracters for an count use it together?

Yes all your characters on an account use the same Menagerie.