I used Android Market back on the Atrix 4G (early 2011) and don't remember a time when there weren't categories and various 'most-popular under x criteria' lists, but regardless, they certainly do exist now. You can also see a list of similar apps when you view any particular app.
I agree that any of those old Android phones running pre-4.1 are slow, and would wager that the slowness is a guarantee. My Atrix 4G was the first dual core phone, had the most RAM (1GB), lots of internal storage (16GB), and blew away every other Android device on benchmarks for months. Even so, it was and still is slow as fuck. I can't imagine how bad competing phones were at the time. That said, Google did Project Butter as of 4.1 and then Project Svelte as of 4.4 with the primary goal of making everything smooth and fast. Needless to say, things are much better now.
When your fiance's phone had trouble charging, was she using the stock charger and stock cable? I only specify stock because those are guaranteed to be "good enough". Otherwise, the chargers and cables people buy can come from a grab bag of quality levels that I wouldn't even bother trying to analyze. The short answer is, use proper equipment. My dad has the HTC One M7 and has had problems charging too, but we didn't get mad at the phone. We just replaced the charger with one I like A LOT:
http://www.amazon.com/HP-North-American ... B0055QYJJM
FWIW: I specifically didn't want to use the stock charger because it makes a clicking noise when unused (same with the Nexus 4/5 charger) and it annoyed me too much.
You said "all kinds of problems" but the charging thing is the only one you mentioned..
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