Dark Element fights similarly to Dark Genie. DE opens with BFR but note that DE goes with the opponent to said dimension. It then summons 5 Dream Monsters to fight it's opponent, these 5 monsters are comparable to DE in power but they have no hax so they will physically try and fight Shantae.
If these five monsters are defeated, DE will fight and it's tactic is shooting dark magic arrows or swinging it's staff, increasing it's size and shooting a massive energy blast. DE doesn't use it's more useful hax in character and even when he's about to lose he still doesn't.
1. Close Combat from what I can remember, I'll check later in the morning.
2. It would likely be surprised at first but unlike Dark Genie, Dark Element actually moves but he doesn't spam teleportation, it's just something he does in order to get some distance. All in all it wouldn't be to much of a problem but given his to most used attacks are ranged attacks it would be an issue.
3. Given how Dark Genie/Dark Element is resist to dark magic do to it being within him and it is shown Holy > Dark in Dark Cloud verse, yes, Holy Magic will be super effective.
Ok so Dark Element will start the fight with thought based BFR which emits a white light from himself and both end up in another dimension. Note that Dark Element will place Shantae at the bottom floor while he is at the top and she will half to face off against 5 monsters, each comparable to Dark Element and that means they have the AP advantage but not nearly enough to one shot.
Luckily Shantae has some good abilities on her side. These monsters will face of against her one after the other but 4 and 5 fight together so she will face both of them. Do to her Attack Reflection, she can easily reflect their ranged attacks and do to them being quite large monsters with no real fighting skills she should be able to take them out with not much effort along with summoning those weapons around her to damage them when they get close or just sneak past them with invisibility and go straight for Dark Element.
Dark Element is the only real threat. In close combat he will try and swing his staff at Shantae which she should be able to dodge without much difficulty. Seeing that she is better than him in combat and the fact that she would have weapons protecting her, Dark Element would try to range attack her with Dark Arrows and or a massive energy beam. However they will get reflected so Dark Element will backed into a corner. He can teleport but he doesn't spam it and making himself bigger will just make him a bigger target.
Shantae also has light magic which will do massive damage to DE. The only real issue Shantae will face is DE's hax but as I stated above DE doesn't use it hax in character because it is overconfident to a massive degree which was Dark Genie and Dark Element's downfall. This is do to them knowing they are just avatars and will never truly die. Dark Element may not have Dark Genie's resurrection do to being all of Sirus's hatred in physical form, he is still the embodiment of hatred and unless you get rid of all hatred, Dark Element will return but this is non-combat related for it unlike Dark Genie.
So I'm voting for Shantae do to being a better fighter, Light Magic which will cause serious damage to Dark Element, Invisibility which can catch him off guard, weapon summoning for protection and barriers that can reflect his ranged attacks plus she has healing if she gets harmed. Lastly Dark Element is so overconfident it is not even funny, he will think she's nothing which will lead to his downfall. This is not a stomp though cause she can't one shot and there is the possibility Dark Element will use it's hax but I think Shantae would finish it off before Dark Element is pushed that far not to mention it doesn't really care if it dies anyway which is apart of it's problem.