You will have to determine how the refrigerator is secured so it doesn't move. Check the bottom to see if the support feet in the front have any type of attachment. Same with the top and side.
The refrigerator should be able to be pulled in and out since it is a residential.
Make sure the support you are fabricating is the right size for the wheels to rest on it and hopefully the same height. I would use some cross members to make it into 1 structure and try to secure it from moving.
Take everything out of the refrigerator to reduce weight.
Check to see how the water is hooked up if you have an ice maker. In most cases they will use a length of tubing to be able to move fridge in and out but you'll have to check.
While you have the refrigerator out take the time to clean the cooling fan area and condenser. Over time it will accumulate dust, dirt, etc that reduces efficiency.
I actually just installed a residential, it was elevated about 8 inches off the floor since I have the furnace underneath. I took the time to make a wheeled dolly with platform on top to make it easier to get the fridge in and out. This worked well as I had to move it in and out about a dozen times while I completed the install and moving the furnace in and out.
There are a number of resources on line to be able to help diagnose problems. Just use the make model of the appliance and you'll find sites that have the parts diagrams etc. Check several sites for the best prices. Youtube is another good site once you figure out whats wrong. I've used these to fix stoves, microwaves, dryers, washing machines etc. A rudimentary understanding of how to use a multimeter helps.
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