Try making coffe. I think his Confidants locks at rank 4 until a certain point in August.
I say do the palace as soon as possible, or if you decide to leave it at last make multiple save files just in case. Technically it takes at least three days to complete a Palace: 1st reach the treasure, 2nd send the calling card, 3rd fight the boss. Since it's the first Palace, it's probable you can't reach the treasure on one day due to SP, so don't feel bad about visiting it a few more times.
As for Confidants, yes, you just need to talk to the person to activate the Confidant event (if possible, have a Persona that corresponds their Arcana, (have a Agathion in your Persona inventory in case you want to hang out with Ryuji because he's Chariot). Then depending on the answers you give them during the conversation you'll gain points to keep continuing their Confidant faster. I recommend doing the Doctor Confidant since she eventually gives you SP accesories to buy.
Other things you can do are activities that increase your social stats. You can make tools for Proficiency, go to Diner/study at the library for Knowledge (I don't remember the exact floor the library is but I think it's next to the Student Council Room?), visit the bathhouse for Charm, etc. These Social Stats are neccesary to activate/continue Confidants, for example Ann requires Rank 2 of Kindness to hang out with her.