That cloak is dropped from Luceria. Probably can find someone that would sell it, I don't know the price. You can get people to craft it too if you can get some urns.
Name is probably Cloak of Luceria
People do sell astros to others, generally you pay, then they gift or vice versa. It is filled with scammers and technically against the ToS, but do it at your own risk.
To get a weapon from a boss, it's pretty rare, usually around 0.001% to 0.01%.
Adding Rare item Drop Rate only increases the chance that if an item drops, it will have more options. It does not change the amount of drops, nor the quality of it.
You want Item Drop Rate for more drops.
Guitars, I would add Magic Min/Max , then STA, or LUK, or w/e
Music Rods, again, Magic Min/Max