If you go into your Collection and then achievements, you'll see that unlocks are tied to different things. For example, if you want a certain song, it's tied to getting a 10K/20K etc combo. If you want an NB Ranger calling card, that's tied to Mission Mode.
It may seem like Arcade is giving you a ton of things but thats because you're doing different things in Arcade. You may be getting S/A ranks, you may be playing on Normal difficulty, you may be activating Fever a number of times. So you're accomplishing different things, hence all the unlocks.
There are 776 items so you'll always unlock something.
If there's another way to unlock things, then I'll be surprised as well. Glory Day was unlocked at level 25 and that wasn't anywhere in the achievement lists so it's possible.
Yup. Hamsin needs to be unlocked by playing and clearing x amount of MX songs.
Memory of Beach should be playable from the start.