what are the events of the cell cycle in correct order, names, and specific steps of mitosis & what happens in each? connection between cancer?

The above answer is correct, but a bit short of details. 
Just remember IPMAT.  Make a word of it.  That's it.  Interphase, prophase, metaphase
anaphase and telophase followed by cytokinesis.

Think of it
this way: 

The "I" is for
inter - meaning the cell does what it does.  It is "in
between" mitoses.  If its a neuron, it conducts electrical pulses.  If its a beta cell
in the pancreas, it secretes insulin, etc.

The
"P"  means the cell is
"preparing" for mitosis.

The
"M" means the chromosomes are moving to the
"middle" of the cell.

The
"A" means the chromosomes pairs are moving
"apart"

The
"T" indicates that the chromosomes are at the
"tips" of the
cell. 

Cytokinesis means the movement (kinesis) of the
cellular contents (cyto)

Hope this
helps.