One of the fastest ways to improve at osu!mania and many rhythm games in general is to learn what your weaknesses are, isolate them, and get better at them. If you're weak at streaming, find maps that have lots of stream in them. Better yet, learn to use the osu!mania editor minimally, and create a map that has nothing but 1/4 streams, or 1/8 streams, or... whatever tempo/speed you want to practice.
If your problem is a specific part of a map, osu!'s editor makes for a great and safe way to practice certain sections of maps. If for any reason you accidentally alter the map, osu! will force you to update back to the original version, so there's no fear for cheating. Those two things alone can help substantially.
A mechanical keyboard is certainly not required. I was playing without a mechanical keyboard for quite some time, and recently got a mechanical keyboard for Christmas. With that being said, I love my mech and will have a hard time going back, but you should by no means feel like your skill will be impeded without one. It's better for those who have played on membrane/scissor-switch to move to a mechanical because they'll know how much less force it truly feels to trigger keys in a high-density sequence.