Here is how I fix cupboards that have swollen particleboard areas like cabinet doors. You can repair them if the edges have not expanded to the point of ruining the sides of the door.

You are going to need to get some lacquer thinner and have some type of squirt bottle to put the liquid into. This will be used for separating the glue from the two surfaces. read How to Fix Swollen Cabinet Doors

How you fix a loose area on your cabinet is going to depend upon where the wood joints are that are in need of some glue. Check out this fast drying wood joint glue that will repair many problems with crown molding seams and even face-frame separations. A word of caution though, this glue dries like super glue fast, strong and hard.
read How to Fix Loose Cabinet Wood Joints

Most of the cabinets that people purchase off of the shelves from Home Depot come without having solid backs on them. This of course depends upon the brand and style of cabinet that you are considering to purchase. I would suggest that you ask a sales person if the cupboards that you are looking at come equipped with solid backs on them. Most of the upper cabinetry should have solid pieces of wood in the back so that they can be hung on the wall. read Do Cabinets From Home Depot Come Without Backs

If your cabinet installer did not put a hood vent cover over the duct work then you need to inform the company you purchased the kitchen cabinets from. It is not acceptable for the raw metal duct work to be exposed inside of the upper cupboard over the range. It is tacky looking and poor craftsmanship. There are no excuses either for any company doing such a poor job.
read Does the Cabinet Hood Vent Usually Get a Cover?

I have been custom fabricating kitchen cabinets for over twenty seven years.
Manufacturing dimensions (sizes) fit into specific standards that are repeatedly used. Let’s take a look at what measurements are commonly used for building kitchen cupboards.
read Kitchen Cabinet Manufacturing Dimension Standards