yes they make chains for snowblower tires. screw in teh tire is a
interesting idea not sure if i would do it my self

No the tire you have are made to be used with no chains. The rubber is
softer to help with traction also with the big knobby tires chains will just
end up between the knobs and become ineffective.

yes tire pressure will make a difference should be 12 - 15 psi but double
check on the tire itself it should have the rated psi for your specific
tire.