I'm no expert but they look like proofs to me. If they are not they all have good strikes and high grades. No matter what we say though your best bet is to haveMULTIPLE dealers check them because pictures cannot replace holding the coin in hand. Either way great set niccce! I do agree with kirk about the quarter though looking bus. Strike but could be pics.
I know the pictures are not good. I am using an Ipad camera. I do have some MS 65 MS 66 and MS 67 coins from the 1940s I am comparing these to. In any event I will take this into a local shop and see if they can help.
Sorry to tell you but that's a mint set. The rims are rounded, not squared like you would see on a proof coin.
I wish I could help u with the gold tract but I can't offer knowledge I don't know enough of ..someone will chime in give time.
The cent definitely looks like a proof. I can't say anything about the others because I don't really know the characteristics of proofs from other denominations.
I ask again, what has you so convinced? Though it has been stated that the coins have rounded rims, hey look pretty square to me. I have proof sets dating back to the 1870s, so I know a thing or two about proofs, but I'm always open to learning something new.
I can misjudge from poor photographs just like most anyone else . . . therefore, I relied upon the sharpness of the rims for my conclusion. Much better photos of the OP's coins would almost certainly change your mind.
Judging from photos is most difficult indeed. There are a lot of knowledgeable fellows posting here. If only we could examine the coins in hand..........
My opinion is that Washington Quarters of this era were NEVER particularly well made. In all of my years of searching for early cameo proofs, I only ever saw one that I truly desired . . . a 1939 that I walked away from for 15 minutes to think over price, and I've regretted that hesitation ever since. NEVER rely only upon the depth of reflectivity of Washington quarters to determine proof status, as most exhibit a satiny cartwheel and mediocre mirrors.