It’s similar to a bunch of the threads I’ve seen but it seems like there’s a different solution for each course.
I’m on Level 1 (26/28) and I can’t learn new words it just seems to loop between pronounciation and meet the locals.
Try and go to the next level and start learning from there. Also, instead of letting Memrise decide what to do next, select learn/review/speed/etc. manually. For instance, in the app, tap the three dots, then tap i. e. the learn icon.
Are you learning from English? There are grammar lessons for some English courses, those lessons are counted as ‘new words’ and they are unavailable for the web, but it should work OK for the app. Do you have a subscription? If no, maybe that’s why you can’t access them and see this message.