Some of this is not a training problem, and treating it like one wastes time your dog may not have. If they are distressed when you leave, if they growl or guard their food, their toys or you, if they are frightened on the lead, or if anything about them changes suddenly at any age, contact your vet the same day. A tip from a website, ours included, is not the answer. If it cannot wait, contact your nearest emergency vet now.
With an Italian Greyhound, watch their legs and their mouth. If they suddenly hold up a front leg after a jump, contact your vet now. Bloat (GDV, a twisted stomach) needs the same speed: a swollen, tight belly, retching with nothing coming up, sudden restlessness or drooling. It can happen in any dog, though it is most common in large, deep-chested breeds. A skip in a back leg can be Patellar Luxation (PL, a slipping kneecap). Bad breath, dropping food or chewing on one side can be their teeth. Bumping into things at dusk can be Progressive Retinal Atrophy (PRA, gradual loss of sight), which is a known risk for the breed.
They'll want the jumper all year. If they jump off the sofa and hold up a leg, contact your vet now.