There are a number of questions being asked here. I'll try to cover most of them. I'll start with the last question about whether or not Bassanio has an unfair advantage in choosing the right casket due to Portia's hints. The answer to that is "yes." If he got hints and the other guys did not, then that is an advantage; however, I would argue that Bassanio is not given enough of a hint (if any) to make a difference in the first place. I've seen it argued that the song is supposedly a hint that Bassanio should choose the lead casket because the song has several words in it that rhyme with lead, but I personally think that is tenuous at best. Secondly, Portia admits that her loyalty to her father is strong enough that she is unwilling to give Bassanio any hints, even though she very much wants to do that exact thing.
I could teach you
How to choose right, but I am then forsworn.
So will I never be.
Bassanio's logic for choosing the lead case is that beautiful appearances often mask inner ugliness. This is why he does not choose either the gold or the silver boxes like his competitors did. They believed that outward appearance was most important, telling, and representative of Portia. The fact that Bassanio correctly chose that outward appearance is secondary to the inner prize does seem to indicate that Bassanio is the type of man that Portia's father would intend for her; however, Bassanio's logic stands in stark contrast to the man that we were introduced to. When audiences first learn about Bassanio's attraction to Portia, we are given two main reasons why he wants to woo Portia and obtain her favor. She is beautiful, and she is rich. He has no idea what kind of inner beauty Portia has or doesn't have. His logic in choosing Portia to chase is exactly in line with the other suitors.
In Belmont is a lady richly left,
And she is fair and—fairer than that word...