Question 1 - How many Kryptonian ships were there, anyway, and what happened to them? This is my count.
1) Clark's ship that took baby Clark from Krypton to Earth and ended up in the Kent barn. Its Phantom Drive was used to get rid of the bad guys. Outcome: destroyed.
Yup
2) Zod's ship. Sent back to the Phantom Zone with all hands (except for Zod). Outcome: off Earth and no problems for us anymore
Yup
3) The World Builder (which had been piggybacking on Zod's ship) - destroyed by Clark. Outcome: in shards? Or being taken by LexCorp to have all its Kryptonian technology dissected and analyzed?
Yup, and oh dear. Lex is bound to try and and get his hands on it. Although would Clark get rid of it before Lex had chance to set out any salvage operation?
4) The scout ship at Ellesmere Island that sent the distress signal that lured Zod to Earth. Did this ship get destroyed too? I thought it was going to be up there at the North Pole serving as Clark's Fortress of Solitude, with Jor-El as its AI. But am I mistaken? Did it really get destroyed, and is Clark now alone on Earth as the Last Son of Krypton, with no Kryptonian technology to back him up?
This is the ship that Zod went to find knowing it had a Genesis chamber on in. Zod put his own comand key in it to overwrite Jor El then he flew it into the battle. He was attempting to shoot down Lois and Hamilton when Clark arrived after taking out the World Engine. It crashed into Metropolis with Zod still on board, which is why Zod wasn't pulled into the Phantom Zone.
So. It's in Metropolis. See previous answer. Lex will want it, but hopefully Clark will take it off someone first.
Question 2 - Dr. Hamilton and Col. Hardy either died or went to the Phantom Zone along with the Kryptonians, right?
Yes, it does seem that Hamilton and Hardy have ended up in the Phantom Zone. Hardy wasn't dead at the point they actived the rift and Faora won't have the superpower advantage once they are in PZ so it's possible he's still not dead. Although what life is like in PZ and whether they can escape from the Kryptonians is unknown. Plus how with the Kryptonians behave without their leader?
Question 3 - Clark used a Phantom Drive when he was an infant. Why didn't he get pulled into the Phantom Zone along with the other Kryptonians?
When he was rescuing Lois it was a strugle to get away. You can see 'lightning' striking across his face as if he's being drawn in. So, if flying is strong enough to escape the PZ pull maybe some other Kryptonians escaped then? NOPE. All the others were inside their ship (and Faora in the plane) not able to set of flying before the gravity got them. Also, my husband pointed out yesterday (at our 3rd viewing) that Zod had to remove his armor before he finally figured out how to fly. It seemed to be interfering with whatever effect flight has on gravity. Faora and the other Kryptonions never flew once in the film, just leapt.
Suitable answers or not?