Changing resolution should be fairly trivial, the battle controller sets things up based on the room size and most menus are defined in terms of two constants VIEW_W / VIEW_H. You'll need to manually change room sizes / viewports of every room in the game, but there's just a handful of rooms so it's hopefully not too much work.
Overworld character speed is defined in pixels per step, but it's just one variable you need to change in the player's create event. You might potentially also want to change the TILESIZE constant if you change the tileset size (this will have some ripple effects like grid sizes in existing rooms also having a different size, but I've never really tried changing a tileset size so I'm not 100% sure how much of that is automated)
Attack animations uses any object you want (typically a child of the effect parent), the battle flow waits until all effects are gone before proceeding. There's a convenience script fx_deferred_projectile which lets you spawn a standard projectile which runs another script on-hit (which works for a wide range of attacks) but you can add as intricate effects as you want if you feel like it.
The movement system isn't grid-based, but it shouldn't be too hard to add in. You'd basically turn the overworld player into a state machine with two states (idle and walking): in idle state, if any movement key is pressed, if whatever's one tile in that direction is OK to stand on: switch to walking state, start a countdown of TILESIZE, and start moving in that direction. In walking state, reduce the countdown, and when it hits zero, stop moving and switch back to idle state.