10-30 or 30
How to Change the Tires on Self-Propelled lawn Mower
blade might be out of balance
SAE30
I've never owned a self-propelled mower, but I would think there would be a lever to engage the wheels for self-propulsion. If the lever is in neutral. I would think you would be able to pull the mower backwards on all four wheels. If there is no lever and the mower is self-propelled at all times, you would have to raise the wheels that are propelled in order to pull the mower backwards.
There is usually a clutch which disconnects the motor from the wheels. That will make it ok
SAE 30 full synthetic oil, any major brand.
you can't unless it has a lever that says how many speeds it has
SAE 10W30 any major brand. I recommend you use synthetic oil in any air cooled engine.
That would depend entirely on the particular Toro mower you're referring to.
How do you change the blade on a Toro 21" self-propelled mower
Honda, Black & Decker, Husqvarna and Fiskars are all well rated self-propelled push lawn mower manufacturers. Not only do they A difficulty with some self-propelled lawn mowers is that they are often still fairly heavy, so they can be difficult to maneuver, so you might also consider a well-designed mechanical (non-powered) type.
You are Supposed to be able to do that easily. Oil the wheels. What is keeping it from moving backwards? Look fer it!