With the float bowl overflowing the engine runs rich, and the richness increases as speed decreases. Hence you cannot expect it to run properly until you get the float bowl working.
If it floods, the needle is not closing properly against the seat. The most common reason is dirt in between the two parts. However it can also be due to the float arm being stuck (the part the float lifts up, and which in turn lifts the needle until it presses against the seat).
One of the traditional ways to check the operation of the needle and seat is to remove the carburetor, empty it, turn it upside down, and suck on the fuel pipe barb. If you can suck air - even a tiny amount - it isn't working. To work properly you have to get it so that you can suck some vacuum then put your tongue over the barb and wait to see how quickly it loses the vacuum. It should hold for quite a few seconds.
It is OK to run the mower with no blades, so long as the blade plate is installed.
