Plothole!
But to give you an explanation I would say that most of Krypton didn't believe in Jor-El's theory and it's quite possible the Kryptonian Council also had a tight control on the population and what they could and couldn't do. In a lot of comics, cartoons, etc. basically everyone thought Jor-El's research about Krypton being doomed was a joke and didn't believe him.
Plus a mass migration takes A LOT of planning. Krypton's destruction hit like a surprise earthquake or a tsunami. The Kryptonians were so arrogant and confident in their planet's stability that they didn't believe Jor-El. It's quite possible the Krypton Council put a ban on certain space vehicle and hence why Jor-El constructed one in secret.
Yes I know there were a lot of ships flying around during the battle scene but those were under Zod's control.
The Codex is essentially the encyclopedia of Krypton. It contains all knowledge of Krypton's life, culture, technology, etc. Jor-El was infusing it with Kal in order to preserve their entire culture and knowledge with the "Last Son of Krypton" and
hence why Zod was after him to "recreate" Krypton because all the knowledge was stored within Kal's DNA/body.