Why didn't he shoot Todd?
After they were done burying the cleaning lady.
Because Jesse was afraid of Todd... trauma?
Because Jesse thought Todd left the gun (perhaps not loaded, like he thought the 911 call was also fake) on purpose, even though Todd seemed to be genuinely afraid of the situation... but Jesse was not 100% sure? If Jesse had pulled the trigger and nothing came out Todd would have beat him worse than ever before.
Perhaps a little of both, he was so f'd up mentally that he couldn't think straight.
Also, do you think Todd did bought the pizza/beers? I don't.