You shouldn't be able to sell the speedo, since it's a quest item. The chest at the Pine Island beach where you jump into the water to meet the giant turquoise slime does have a speedo as well, and so does the one in Piratetown near the underwater entrance. Unless you already got a speedo in your inventory, then those chests give you 150 gold instead. Check your inventory again to see if the speedo is there anywhere, or maybe another one of your characters is wearing it? You need to equip the speedo to the Adventurer for it to work.

The two doors are events at the fire- and water dungeon. To unlock them, you must finish each dungeon at least thrice, and collect the loot from the chests in Rubyro's/Saphura's throne rooms every time. Once you got the full armor set of one god, you get their event. Don't worry, the armor chests aren't random, so you only have to loot them three times. For the last four pixel animations: You need to defeat Shaun in the pirate hidehout by making him horny. To do that, you need to defeat Klaus and Dule Dile during his battle first, so he's there by himself, and then use the acts to horn him up. Then, when you leave the area, you get a cutscene where Shaun bones either Dule Dile or Klaus, which one is random, and each one of them got a pixel animation of their own. For the third one you need the gold badge, so you can accept the quest guild quest to defeat Captain Hogger in Piratetown. After you've done that, you can just talk to him to get his scene. The last one is the Demanding Foreman. Just talk to him in the Paradino mines after you defeat Richtor. You can check the walkthrough for more details.

It's an event with Gruffe. You need to unlock his "Bound And Ready" event first on the second Fire Dungeon floor, then talk to him in the quest guild in Piratetown. After that, he appears in a room on the third Water Dungeon floor.

There's an open window at the side of the bull shopkeeper's house in Shiptown. Interact with it, and Wulfrick will help you up.

It's in the third room of the second level of the Deep Mines. You can check the walkthrough for more details. 

0.21.1 is the most recent public version of the game. If you're playing that, you've already reached the end with Richtor's fight. If you wanna support Spedumon on Patreon, the latest version there is 0.81 (the Patreon version has a different numbering system than the public version, it's not 60 versions behind). Otherwise you gotta wait til November for the next public update.
In order to keep your save files, you must copy the entire "save" folder within your current game's folder (which is inside the "www" folder), and use that to replace the one in the updated version.

You need to finish each repeatable Quest Guild quest in Piratetown at least once (all nine of them, you'll need the golden badge for the 3-star quests). Then Buba will ask you to talk to Vulfox in the guild lounge. You can check the walkthrough for more details. Sword is the leader of the royal knights you met in Safen at the beginning of the game. So far, there's no use for the key yet, both in the public and the Patreon version.

I don't know how to help without more info, have you checked if there is a save folder inside the www folder? What are you playing the game on?

It's in the log forest on the first island.

You need to finish all the Quest Guild quests on Paradino and then talk to Rexardo in the Quest Guild Lounge.

They only tease what's going to happen in the story in future! Like a mystery!