No, when the Steamboat Willy copyright expires, there is no longer a copyright which prohibits people from making or distributing additional copies of the work, from publicly performing or displaying the work, or from preparing new derivative works based on it (such as a new Mickey Mouse short in which he commands a homemade submarine powered by barnyard animals or something)
Categorically false. Someone could make a derivative work of the Disney short and call the title character something other than Mickey Mouse, but if they tried to call him Mickey Mouse, Disney could take action against them for using their trademark without permission. In fact, if Disney did *NOT* pursue the matter within a certain period of time, then they *WOULD* risk losing trademark protection (as far as I am aware, the law is not definite on the exact period of time allowed, but it is clear that it is not very long, and the matter would be up to a judge to determine if they had responded with due haste to the matter). It is also worth noting that trademark, like copyright, can be satired within the allowances of intellectual property law, although slightly different metrics are used on trademarks than with copyrights to determine if something that may be construed as an unauthorized copy of a trademarked image or character is actually a satire. A titular character that was called "Mickey Moose", for example, would probably be recognized as being satirical on the Mickey Mouse character because the Mickey Mouse character is extremely well known, which is one of the factors that governs satiring or parodying in the case of trademarks (but is not an issue in the case of determining satire or parody for copyrights).
Ultimately, copyright and Trademark are two wholly different pieces of intellectual property that govern entirely different things, handled almost entirely orthogonally to eachother, and in practically all cases, one has absolutely no effect on the other. Trademark infringement comes into play when ownership of the trademark itself is somehow challenged, which is not caused by distributing a copy of a work, because it is copyright that governs the copying of such works, and not trademark. *IF* Disney were to have trademarked the entire cartoon, then it would continue to be illegal to copy it, but such things are not eligible for trademark protection.
The only way that trademark could possibly be affected by Steamboat Willie falling into public domain is if that would or might cause the public to not realize who Mickey Mouse belongs to, but since the copied work is still a *COPY* of the work, and so would still be clear who owns the intellectual property that is still very much alive.
Be aware that the copyright status on the short has already expired in several countries that do not practice the copyright durations the US currently has in place, and the cartoon can be freely distributed or copied in said jurisdictions, while the trademark status has remained entirely unaffected.
I am not directly familiar with the Shredded Wheat case you mentioned, but I would imagine that the reason the term Shredded Wheat was allowed to be freely used after the patent expired is because the terminology accurately described the product in the first place, and so once the patent expired, the trademark status on the term that referred to it became superfluous. As a counter-example, while Lego's last standing patent on Lego bricks expired in 1989, nobody else that makes so-called compatible building blocks is allowed to call their product Lego, nor are they allowed to even explicitly say they are compatible with Lego (even if they are) without first getting permission from Lego to do so (and they would be extremely unlikely to receive such permission, since they would be a direct competitor), because Lego still holds trademark status on the term in the context of a toy (and also as a company name).
Of course, if Disney had trademarked the title "Steamboat Willie", they would lose certainly lose trademark protection on that title once the work with that fell into public domain.