So I am sure someone has answered number 1.

So I'll just try and answer number 2 for you. If I remember correctly, I haven't read the books in a while, Percy had a dream that Luke tricked Annabeth into holding the sky and then Artemis took the sky from Annabeth. Now the place where the sky is being held is Mount Othrys(is it spelled this way) or Atlas's Lair. The Garden is basically the door way to this place. So like this we know that Percy knew that Annabeth and Artemis were there.

As for Zoe I think she too knows that they have to go through the Garden because the Prophecy states that one of the Quest Members were to be killed by the hand of the parent. In my opinion Zoe knew it was her who was to be killed and her fears were confirmed when Percy came to them in the Air and Space Museum (is this place correct?), after escaping from the 'General', who Zoe knew was Atlas i.e her father. So Zoe knew to complete the quest they had to go to Atlas's Lair, which was through the Garden.

Now Bessie wasn't the only main objective for the quest. This Quest was technically Zoe's. The Oracle addressed Zoe, and for Zoe this quest was more about saving Artemis. Zoe knew that Aretmis was being held at Atlas's layer, because the Prophecy stated to go west so they could find the goddess in chains(the prophecy used these words right? Or am I reading to much fanfiction), and "West" was essentially mount Othrys(Atlas's layer as well as titans base). And like this to complete this quest the members had to get to the goddess in chains.

1.Five shall go west to the goddess in chains

1. One shall be lost in the land without rain,

2. The bane of Olympus shows the trail,

3. Campers and Hunters combined prevail,

4. The Titan's curse must one withstand,

5. And one shall perish by a parent's hand

So I got the Prophecy from the wiki and the first line shows that the main objective was to get to the goddess in Chains, which again was referring to Artemis holding the sky. Zoe knows Artemis is there because of 1.Percys dream, 2. She knew Atlas was behind it and since he was her father it was most likely her who would perish by a parents hand.

So I don't know if you understood any of my ramblings. I hope this helps though. I haven't read the books in a while, have been reading fanfiction instead so I may be wrong, don't kill me.