Pretty much every shipyard can sell/buy hulls and/or repair them, though some shipyards (the pirates notably) only offer limited choices of hulls. I don't understand your problem.
AFAIK, the only shipyard 'improvement' you can make to your current ship is to upgrade the cannons. Click on the calibre of cannon you want installed in the shipyard screen (listed on the left), and a button will appear giving you the choice to do it or not (if you have enough cash). Some ships only allow 12-pounder cannon, so you can't upgrade to better cannons on all ship types.
All other 'improvements' come from the skills you choose to increase at level-up and/or the officers you have hired. Hit F1-key, then go to 'staff' tab to see.
There is an NPC you can talk to wandering the streets of Highrock (Albrecht Zalpher) who claims to have developed new improvements for ships. If you answer him wrong, he gets suspicious and leaves the game permanently. If you answer correctly, he offers to join you as your ship carpenter. But if you ever subsequently land in Tendales, he leaves your ship permanently and gives you his 'plans' in exchange... you can sell those plans for 1500gp at a shipyard or take them to the governor, but there is no other 'reward'. His plans unlock nothing in the game.
Post edited April 25, 2020 by Dreamteam67