Fortunately they don't cook cook him. Unfortunately he's a raw dessert.

Interesting question. Нам is dative, so I (and I'm totally guessing) think the verb would have to change at the very least. Maybe to reflexive?

But then it seems like the meaning would be: The borsch is being prepared by us. Same basic meaning but maybe a different emphasis?

But, again, I could be reading too much into this and be totally wrong.

The remembering this is going to all be on you. It's hard to remember to take all of that into account but as for understanding:

Check out the subreddit for learning Russian language and culture

It's best if you create your own charts for cases 1) because you'll understand your own charts better and 2) online charts are rife with errors.

That said, if you want a chart to start with this chart, though I still use it, falls apart in places but is mostly ok with singular cases, pronouns, and most adjectival stuff. It's a decent start to figure out how you want to craft your own.

This is the best I can do to help you, next time try to be more specific on where you're falling down.