All of your questions vary depending on the type of insulin you are using.
While Novolin is often a choice by vets because it is a price people can handle it isn't the best for cats because it is a short acting insulin with their metabolism so it can leave them in high numbers after the insulin has worn off or could require shots more often than 12hrs apart. Some people are able to get a reasonable regulation with Novolin, but the longer lasting insulin like Lantus, Levimir, and ProZinc tend to have better regulation and have reported better remission rates.
You can always switch insulin if the one you are using isn't working. Before switching, you want to figure out if the one you are using isn't working for you. We recommend home testing and there is a spreadsheet we use on this forum to help us track and analyse the testing. You can see links to them in most of our signatures.
Insulin does degrade after a while. I don't know the details on Novolin since I've never used it. There should be some information on the packaging. With Lantus we know that if we keep it refrigerated and handle it carefully we can use it well past the recommended 28days on the packaging, I don't know if that is the case with Novolin since it is a different mixture. Someone who has experience with it should chime in.
The short acting insulins like Novolin need feeding close to the shot time because the have a quick and harsh onset. Having the feeding that 30min before the shot allows for the food spike to be kicking in at the same time as the insulin spike so that you soften that sudden drop. Without the food, you will see that hard sudden drop the insulin is known for. Some of the longer ones it isn't as important. We still try to make sure our cats are willing to eat, but we usually test, feed, and shoot all pretty much at the same time.
Moving shot time. The depot insulin like Lantus and Levimir thrive on consistency and any movement in shot time acts like an increase or decrease in dose. For those we try to move shots only 15-30mins at a time. For in-and-0ut insulin like Novolin, it is easier to move shots because once the insulin is worn off, it is out of the system and you don't have to worry about overlap or depot as much. You want to be home testing if you are moving your shot up to earlier so you know if it is safe, but you could probably move your shot time 1-2 hrs at a time if the numbers weren't to low. If you need to go later, you will just be leaving him without insulin for longer.
Browse the site and read lots of the stickies. Whatever insulin you consider switching to, go to that insulin's ISG and read the stickies there.