I'd suggest wearing the suit. Make sure it is clean and pressed if you can. Black can show up all sorts of fluff etc so use a lint roller or sellotape to remove any bits before he leaves.
I'd definitely go for the white shirt, it will look so much fresher and smarter than the black. Black shirt plus black suit can be really tricky as the two blacks are highly likely to be different making one of them look tired.
Tie fashion is in a kind of anything goes place TBH. They are slimmer than say 10 years ago, but few people wear the truly skinny type. Ideally go for some kind of stripe which compliments the suit and shirt so backs, whites, greys and or blues. I wouldn't put a plain blue tie with a black suit but if it's part of a stripe pattern it can work well.
I can understand why your son would resist tucking his shirt in. It feels a bit alien to people who are not used to it, but it really is important and will look so much better than untucked.
The jacket sounds passable. It's ok not to do it up if it's too tight, and people generally do unbutton their jacket when sitting anyway.
I appreciate that the job itself would not require smart dress, but I honestly think that a suit in an interview gives a good impression and most importantly shows you made an effort.
Having said all this if you find the suit is really creased, he insists on wearing the shirt untucked etc., he may give a Breyer impression in jeans and an ironed T-shirt.
Most importantly good luck to your son!