Well, it means the same, it just doesn't itself show the gender of the subject.
Not really. I heard that women are more likely to use the gendered version, but I don't know if this claim is based on any real data. For sure there will be situations when you don't know the gender of somebody, so the infinitive version will be useful then. Or you may translate a novel with a plot twist, where for example the reader thinks of the main character Pat as a man but at the end it turns out that Pat is short for Patricia. So also you will use the infinitive version then. It is very difficult to try to make Polish un-gendered, so even with this, that will still be a complicated task to deal with the whole story.
I think you have a bit of a point. In English teaching, Future Continuous is considered one of the more exotic tenses and not taught until B2 level. And five lessons seems rather a lot.
To a certain extent Duo teaches using the discovery method, basically trial and error. And especially in the early days they eschewed much in the way of grammatical explanation.
This could have been a really interesting and novel way of teaching a language. After all what I really need to know is that it's "do szkoły" and "w szkole". A child knows that long before they've heard of "kogo, chego" (Genitive) and "o kim, o czym" (Locative). And personally I try and ignore the over-technical explanations on the comments pages, and just go with the flow.
This would be a really great way to learn a language. But it needs context. Every time. But we don't get much of that in any of the Duo courses, unfortunately.