Tiered Subscriptions and General Feedback
I've used Duolingo for several years now off and on, but more consistently in recent months. Let me start by saying that I love Duolingo. It has done more to help me learn languages than any other software or book courses have. The only thing I've found that's better is having an actual teacher. I greatly appreciate all the work from course creators and staff that have went into this.
An aside before I get to what I think could the make the site/app better: I think the subscription price is prohibitively high. As the title suggests, I think the solution to this could be tiered subscriptions. Some people can afford to pay $10 a month, that's great, let them. I can't. I'm passionate about language education and want it to be free; I want to help support Duolingo and I imagine a lot of other people do too, but aren't willing or able to pay that much to do so. So have another option at half the price ($5 a month), with less benefits, once they figure out what benefits are going to be in general. Now onto other suggestions.
1) Add Tips and Notes to mobile. I think this is the most important one, and I'm sure it's been suggested a million times (I'm extremely new to Discussions (edit: apparently I knew about it 2 years ago and forgot), but here it is again. It just makes sense. I, personally, use the mobile app way more than the website. Having that available would save me a lot of web searching, and occasional frustration.
2) Make the sentences more complex as the course progresses, and switch up the nouns as well. This is mostly directed at the Irish course, but may be applicable to other courses as well. In the Irish course I am around halfway trough, maybe a little over. Sentences are still basically the same structure as earlier lessons. [verb pronoun article object], and certain words are repeated more than others, not only does this hinder learning, it get's boring. We've learned how to add more to sentences, but it isn't often tested. For example, instead of "Bagraíonn an muinteoir na daltaí," (The teacher threatens the students,) go with "Bagraíonn an muinteoir a daltaí nuair a feargach uirthi." (The teacher threatens her students when she is angry.)
3) Having a complied list of words learned, and possibly how often you get them right. The more detailed this is the better in my opinion. This is less about the course, but would help me personally, help me feel like I am progressing. One of the biggest obstacles to learning a language is people feeling like it's impossible to do. Having a word list and seeing "You have learned x words and this is how well you know them" would help me feel better about how much I have learned.
4) Conjugation charts. This is an easy google search to be sure, but having these listed natively on Duolingo would be easier for people learning.
5) Create a Discussions app/integrate it into the base Duo app. I had no idea this site existed until very recently. A lot of more casual users probably don't either. I could be helpful for everyone.
That's everything I can think of at this time. I still think Duolingo is an amazing resource and am so grateful that I found it. I thank all the people that have worked on it and will work on it in the future, these are just things I think could make it even better.
About 3, there is a words tab, but they don't have it on newer courses (probably including Irish.) I agree that subscription price should be lowered. I'd be happy to donate occasionally to Duolingo but I don't want to spend 120 dollars a year to remove ads and do offline lessons. I think that 4 or 5 dollars a month is much, much more reasonable. The other points you made are also valid, and some of them are suggestions I actually haven't seen before.
You can access the Tips & Notes through the mobile browser version. Obviously, this is of limited use for those who don't know there's a website, but you are no longer among their number!
You have a Words tab for French, right? It is pretty much what you subscribe about a list of word strengths. Assuming you've got it there you can access it for Irish, too. Open one browser tab to the French tree (or Discussion). Open another. Switch the language there to Irish. Return to the first tab and click on "Words." It'll be your Irish word list.
The more complicated sentence suggestion is a good one. Yes, it varies by course. My personal weighting of tree quality largely stems from how well a treat complies with a such a criterion.
Using the mobile website defeats the purpose of having an app, programs like this don't run very well on mobile inside a broswer. And there is no words list for Irish, nor is there one for Welsh, and Norwegian which leads me to believe newer courses, the ones added after Spanish, French, Portuguese, German, and Italian, don't have them. Although I didn't know about the words tab for French. If this is true, that is something that should be addressed.
I'd advise you to actually visit the mobile website. I agree it's not great for lessons; the T&N, which is the functionality you were requesting, however, are formatted to look pretty slick.
I'm presume the Words tab wasn't extended because it was found through testing to not be terribly useful. I suspect folks are much more responsive to seeing their trees gold, etc., and rarely look at it. But if you want to look at it for Irish, I've told you how.