A couple of years back i played a game, the name of it i can for the love of god not remember, so im coming to you guys to see if you have some answers.
it's a dungeon crawler i would call it, in a sorta anime style, your team is made of a female and a male characters which you have from the start of the game, the male being a sorta warrior/fighter type and the female being the spellcaster and whatnot. you can teleport to town when you clear the dungeon, in town you can buy your standart equipment and there is a special vendor that has a chance to have some special gear, you're also able to get a pet if im not remembering comepletely wrong, there also was a pvp feature where you could battle other players teams
i realise this sounds like alot of dungeon crawlers/RPG style games now adays and i know it might be a strech but if anyone knows of it i'd be happy.
Was it called The Weapon Masters? Your description immediately made me think of this game. If that's the case, I'm afraid it was taken from the page because the game devs stopped hosting it. Here's a link to the game's quests along with an image that may help identify whether this is what you meant or not. It's at the end of the list in the OP.