Yup, much more clear.
To make a sprite "jump," you need to set the Y speed ($AA,x) upward (80-FF, 80 being really fast and FF being really slow). SMW's movement routines create a gravity effect automatically.
The hardest part is detecting when to jump. Setting the y speed in midair will cause a midair jump, which your probably do not want. Setting the Y speed always will just shoot the sprite into the air without ever coming down.
Here is a simple block of code that will make the sprite jump whenever it touches the ground.
LDA $1588,x ; don't set speeds if not on the ground
AND #$04 ;
BEQ NOT_ON_GND ;
LDA #$D0 ; y speed = D0
STA $AA,x ;
Making it wait before jumping will require a timer.
To make a sprite shoot another sprite, you will have to spawn a new one and set its speed. Download a shooter sprite of some sort from the sprites section and look at the code it uses to spawn sprites. That should teach you more than I can explain here.
Health is a difficult thing to do if you're just starting out. First we must know if damage can be caused by mario jumping on your sprite, by having a sprite (such as a shell) being thrown at it, or by being hit with a fireball or cape. All three things are coded quite differently.