My front porch slab has cracked and part is at least an inch lower. It is supporting the roof. Now there is a crack going up the inside of my drywall at the same place. Suggestions on how to solve this so I make sure it is done right.
You have to jack the porch up to get it back to the correct height. I would suggest using a level to hold at a congruent part of your roofline or front molding.
Take a car jack and a 4x4 and prop the roofline until it is a bit higher (1/8") than level. Slide under some pressure treated wood or rubber shims under the posts. Check in local rafters, connecting pieces and make sure that everything is snug, braces are still work, and so on. You need a really good visual inspection. This is a bit of an emergency since if you wait you could incur a lot of damage.
Now for the porch... There are a TON of ways to go about this. You could just leave it alone and hope it doesn't sink anymore. They won't sink forever even with bad footings. There comes a point where they pretty much stay. Just make sure the dirt around it isn't eroding - if it is landscape to protect the area.
You could also have a new porch poured. They would simply jack up your posts, demo old porch, and pour new.
You could build a wooden porch over old. This would probably require a little demo for the posts. This is only feasible if your porch is a bit lower than your step - or you have to do a total demo. Demo isn't as hard as you think because you can dig a hole and bury most of it in most cases.
People do have their pads injected with concrete to provide makeshift footings. Concrete company will come out, drill through porch in strategic areas, bore deep enough for footing, and pour. The good companies that do this have it down to a science and do great long lasting work. However most never give you a proper footing and it sinks again in 5-10 years.
Really the take away is get it jacked up and then figure it out after. This happens all the time and isn't the end of the world unless you let it go.
Forget the porch, it is a goner. The important thing is to support the roof.
You need to create a footing for the pillar (or pillars) that is/are holding up the roof. Dig 6 feet down minimum make a bed of gravel. Insert a concrete pillar form (you can get them at Home Depot). Pour concrete into form. The footing should be 6 feet or more under the surface of the earth. Put the pillar on top of this footing.
A larger issue is the rest of the house. If the whole house is on a "slab", meaning it has no foundation and no footings, you are pretty much screwed because the same thing will happen to the house as happened to your porch. In that case, basically the house is a raft, not a house. Once the "slab" of the house cracks, water will infiltrate and the nightmare will begin.
Note that there are "crack specialists" who cater to the cracked slab business by injecting stuff into cracks. Its pretty much snake oil, although if you are selling your house it can be useful to disguise the unsound condition of the foundations, but a good home inspector will not be fooled.
You can do all kinds of half measures, but all of these fixes will not work, because the essential problem is that the ground is shifting underneath your foundation. You can inject goo and concrete all day long and as soon as the subsidence repeats the next winter or whatever it will crack again. Whether the cause is sliding clay, sand, frost heaves or whatever, if you just put stuff on top of it, it will crack. To make a sound foundation you have to go DOWN until you reach a stable stratum.