Great list of suggestions! Here's my thoughts on each.
1) I think a mobile presence is good, but should not be games. Apps like for Miiverse and the eShop are the way to go. Apps that can supplement and enhance playing on Wii U and 3DS but in no way replace the experience. I love the fact that I can access Miiverse on the go. It keeps me connected to Nintendo much more than I otherwise would in my busy life. While I wouldn't be opposed to limited demos on mobile I don't see them ever being able to provide a realistic example of the dual screen nature of Wii U and 3DS. A Nintendo Power app that always brings Nintendo news and videos to people's phones would be my dream app.
2) Absolutely no to any Virtual Console games on mobile.
3) Good idea and something I think Nintendo is taking steps towards accomplishing. We've just seen Nintendo Network accounts get integrated on the 3DS (notably shared eShop info) and Nintendo has promised more to come of this in the future.
4) I disagree with your assertion that Wii was necessarily better with apps than Wii U (though it's more a matter of opinion and could be argued either way). Wii had some more, but in many ways I think Wii U's are better. (Note: I am commenting from a US perspective). In regards to video, both systems have the same (Netflix, Amazon, Hulu, YouTube) except Wii U had them from the start and also has TVii as a bonus. In regards to other apps, the Wii Shop Channel and eShop are equivalent. The Nintendo Channel isn't necessary on Wii U as videos are integrated into the eShop and play times are recorded in a separate app. The web browser is significantly better on Wii U. Wii had News and Weather Channels, but I'm not sure how often people really used them and with the hugely improved web browser I think they are somewhat unnecessary. The Check Mii Out Channel and Everybody Votes Channels don't currently have equivalents on Wii U, but I think both could (and should) be integrated into Miiverse. The Photo Channel is the probably the app that I think still has the most useful functionality, but surprisingly has no Wii U equivalent. Miiverse, however, is simply fantastic and in my opinion easily trumps any apps Wii ever had. I would argue Wii U offers the best social experience of all three consoles because of Miiverse.
5) Personally I have no need for physical media playback (other than maybe occasionally photos). I wouldn't be opposed to it being added since I'm sure some people want it, but I think it should be low on any list of changes.
6) There are definitely interesting ideas to explore here. Utilizing the 3DS's success to promote Wii U should be a priority. I like that render of the 3DS player, though I think Nintendo would be concerned about releasing a USB device that reads 3DS cards. The potential for using 3DS's as controllers is big, especially since they have their own processors - you wouldn't need the Wii U to render those additional screens.
7) Promoting off-screen Wii play is a good idea. As for actually integrating Wii into Wii U I think it should be low on the list of changes.
8) Sounds like a solid idea. I don't know if it would do anything about EA, but I'm sure others like Ubisoft would welcome the support.
9) "there really hasn't been a true display of what the GamePad can bring to the table" - I think Pikmin 3 absolutely shows this, but there definitely need to be more.
10) Definitely yes. There needs to be more urgency in releasing titles and it's time to really consider GameCube games as well. This issue is only emphasized by the fact that Wii had such a truly fantastic Virtual Console library.
11) Yes. Capcom recently commented that developing for X1/PS4 is 8-10x more work than last gen. There is potential for a situation like Monster Hunter Tri where the developer thinks it is too costly to bring a project to those systems and Nintendo can convince them to bring it to Wii U instead.
12) Yes, though I think these are coming. Nintendo had some development trouble in the switch to HD, but as those problems get worked out we'll see more games and at a faster rate.
13) If it can be done quickly then yes, but development efforts should be focused on new projects. Yes we had Wind Waker HD, but that was also done as a test experiment for development on the new Wii U Zelda game.
14) More ads are always good. There was definitely a larger advertising push (in the US anyway) before the holidays.
15) I think this would be a mistake and would just add to any confusion at this point. A sticker on the box only helps if someone is looking at the box, not with word of mouth. Any name confusion can be worked out with more ads and with more time. Even if left alone it is something that will work itself out as Wii games, systems, and accessories disappear from stores leaving only Wii U games (and new versions of Mario Kart, Smash Bros., etc appear that kids want and families go to buy). Nintendo should definitely work more to fix this, but time will help and suddenly changing the name will just make matters worse.
There's my thoughts and a lot more typing than I thought I was going to do.