How to alter the laws of physics within Construct
In the event editor, when you click new action, then choose an object, there should be tabs at the top - Platform, Physics, whatever sort of behaviors they have. This is one place I know of where you can alter their gravity, etc., during runtime.
How to make it to where a layer in the back could interact with a layer in the front (like a tank in the background firing at the player)
I suppose you could have a tank sprite in the background, set to be not solid.
Its shots could be non-solid but have collision, and could start small when fired, then they could grow.. Like..
Every 250ms: Shot.width = Shot.width + 1, and Shot.height = Shot.height + 1
Then, when Shot.width is greater than 32, for example, it could check for collisions with the player and so on, then the Shot could be destroyed.
Or you might have to 'Pick object by comparison'.. Shot.width Greater than 32, then do that.
It is an idea, anyways.
How to create a fully functional pause menu complete with the ability to equip new gear to the main character, change settings, and display statistics
In my game, I have a menu layer. My menu objects are global (I believe). When I bring up the menu by keypress, I set the timescale to zero, and set the menu layer to be visible.
Then it's a matter of just using functions that don't require timescale to be above 0. Just immediately sprite X/Y positions, reading single keypresses through MouseKeyboard, things that don't happen over time as it were (like repeating keypresses from 'Key somekey is held', I think).
Then, I think what I did was have a "group" named menu in an event sheet. When I bring up the menu, I enable this group. This way, clicks or key presses that should happen only in the menu happen only in the menu.
Then I set the timescale back to 1.0 and disable the menu group again when I close it.
How to equip items to sprites, such as a change in gear
You can, perhaps, destroy your equipment sprites or hide them when they aren't needed. Then when one is equipped, spawn a new one or just make the equipped ones visible. I am not sure what is best to do.
Then, when equipped, always have the equipment sprites be moved to certain points on the player sprite. You can set "points", with a name, in every frame of their animation.
For example, a raccoon character of mine has a point named "tail" in all frames of animation. His tail object is always moved to Player's point named "tail".
I have certain weapons he can equip. When the sword is equipped, I destroy the other weapons, spawn a sword, then it's always moved to one of the hand points.
When I switch to a bow, I destroy the other weapons and have the bow be moved to his hand point.
How to code special effects to a sprite for things like spell casting
It is possible to alter the parameters of effects during runtime, I think.. You could do that, or possibly clever use of new sprites on top.
I hope I wasn't too confusing, and gave at least some kind of useful answers. =)