Q1: Yes, you are missing an item to do that. Look around the map! As a hint, it's not hidden in the map expansion - you can get it right from the start of the game.
Q2: You need to fish up a something special to reach him. Don't worry, you'll know it when you get it.
B1: Not a bug! Try doing down+jump too :3
With your answer, I have some new questions:
Q1: I get the swap after getting the double jump, that location is not in the map expansion but can I get to that location with a normal jump at the beginning of the game? Compared to the original Celestial, this game seems to lack dash.
Q2: Since I'm just getting normal fish over and over again in Fishing, and lacking a clear target, I checked the code (sorry). According to the calculations, if I need to get the double jump with a 50% probability, I need 266 successful fishing trips. Seems overly harsh on the success rate. (BTW, it actually took me an hour to get the double jump after fishing 136 fishes, so I don't know if I'm lucky or unlucky.)
Q1: Yes, you can get it right away. No items are required for that, just smart usage of Madeline's abilities. There's no reason to rush it though - the second seedbag isn't useful until you get some seeds for it :3
Q2: The chance is low for sure, but that's intentional. This game is more of an idle game than an active one, and it's best enjoyed while chilling out and listening to some music or watching something. If you just want to go for a high score, you don't need to fish for the super-rare catches - farming radishes will give you more than enough income to eventually max out the money counter.
