Your assumptions are mostly correct, but don't always guarantee you the best pick.
For a 18 year old 4 ball B+ vs a 19 year old 5 ball A+, I'm taking the 19 year old based off that information.That said, it's not always right. Also, a 5 ball A+ 18yo is not necessarily better than the same rated 19 year old. There are 3 players in my current draft which hopefully explain both scenarios...
Player A: 5 ball A+ 43 tsp 18 year old
Player B: 5 ball A- 62 tsp 19 year old
Player C: 4 ball B+ 53 tsp 18 year old
Remove the knowledge of their skill points and player C is the bottom of the list. He is 10 tsp ahead of the other player his age and will be similarly ahead of the 19 year old with a season of top level training. The star and grade ratings are based on salary, which can make lesser players look ahead of better players depending on where their skills are allocated.
With having late picks (even factoring bots), I wouldn't invest a lot on the draft. If you've found a 5 star 5 potential player of any age, pick them as your first selection and hope for the best. Even with the first pick, you're relying on a lot of luck to justify getting value for the expense of knowing you have the best player available.