yes the air fuel mix goes down the black tube.
Fuel comes in via the thin black tube and should fill up the bowl.
From the bowl it flows up a tube into the carb venturi to get mixed with air .
The thing hanging off the bottom of the float bowl is a shut off valve and jambs a plug into the bottom of the fuel tube to cut off the supply to the venturi when you turn the mower off.
The magneto is the thing that the spark plug wire comes from and is not connected to the battery in any way so should not get hot when you crank the engine.
If it does some one has buggered the wiring and is feeding it 12V from the battery.
AFAIK the top line mower that comes out of the AYP factory is the 100 series John Deere ( some one correct me if this is wrong ).
The next is the Husqvarnas , then the Craftsman , the the McCullochs , then the Poulan , then the Ropers, then the Rallys
Basically they are all the same, as you get down the line to the cheaper mowers the metal get thinner, the wiring gets simpler ,pivot hole that are bushed at the top end are just plain holes at the bottom end, blades get thinner, control cables loose their adjusters , etc, etc, etc.
Problem is moron sales people tell customers it is made by Husqvarna and is every bit as good without the big brand price tag and because they look so similar people who believe in fairy tales take them at their word then get very upset when they find out that it wasn't quite as similar and robust as they were led to believe .
There is nothing wrong with them, they are just not Husqvarnas.
Go to Briggs web site
Find Your Briggs & Stratton Manual: Small Engines type in your model number and download the parts book and operators manual . FRom evilbay, Craigs List , amazon etc get a copy of the B & S overhead singles repair manual
Go to K & T
"K&T Parts House Lawn Mower Parts and Chain Saw & Trimmer Parts" and scrol down near the bottom to the 3 Poulan links. They will take you to a listing of the owners and some repair manuals, you will just have to scroll down to find your model.
Good luck