Most likely this is a soft tissue injury and not a break or fracture since he can put weight on it but doesn't want to. You can make sure of this by letting him stand and lifting the left leg to see if he will put weight on it. If it is broken he will not put weight on it. If it is a sprain, or soft tissue injury, he will if he has to, but won't like it.
If this is the case you should keep him off of it for about 5 days and let it rest so he doesn't re-injure it or make it worse. Definitely don't want him to jump or run. You can also give him one adult sized plain aspirin twice daily to help with the discomfort.
Let me know if you have more questions,
Probably dysplasia. That may be flaring up, then. That is a problem with the hip joint. The care would still be rest and anti-inflammatory medication. An aspirin will do. The main difference as far as the care would be that you would not have to keep resting him for 5 days. If he has hip dysplasia it will flare up when he is very active and then get better with rest. You might ask your vet for some better medication to keep on hand for instances like this when they are open next week.
As far as the diabetes, the aspirin shouldn't interfere at all with any medications he may be taking or with his blood sugar levels.