There are plenty of crab apples that people eat. Within an orchard variety context if the fully developed fruits are below a certain minimum size then a kind is considered a crab apple, regardless of what other characters it has.

Cutting your tree back would not be expected to change its fruits. If it is a pippin (random self-sown seedling) or one that got onto the site as a root-stock, beneath a named flowering crabapple or orchard apple selection which has since been lost, then it may be producing unattractive fruits for that reason - it having never been chosen and propagated for desirable fruiting traits.

If there is nothing about it you enjoy this tree should be removed.

If i were to remove this tree can i plant a new tree in its place? if not how many feet away can i plant the new tree?

Yes, you can plant another better variety apple tree there or next to it if you cannot dig out.the stump.

If you have enough space you can leave that tree there as your new tree will new a different apple variety to cross pollinate. Crab apples can cross pollinate regular apple trees.

Check reputable on line nursery websites such as Cummins , adam county Nursery, Burntridge, Grandpa Orchard and pick the variety that is suitable for your zone and is disease resistant.

the damage on your current apples are either insect damage or apple scab. Disease resistant apple will help reduce issue such as scab, fire blight, ect. You also will need to learn how to protect youe apples from insects. Lots of them like your fruit.

I will get the stump removed and plant a 4 in 1 apple tree so that they can self pollinate. I dont have much space :(

I was reading online and read somewhere that I cannot plant in same location unless I remove the tree roots.. any tips or advise on that?

I have replanted apples near others that I have removed. Yes something called replant disorder exists in some commercial orchards (one reason why the Geneva rootstocks are suggested). I never had a problem with it.

The big issue is stump grinding. In my area they normally grind down to 12" deep and can go to 24" if requested. This still leaves a lot of roots in the soil.

Sometimes as these roots decompose, the existing site will sink a bit in a few years. I would rip out what you can and have an ax handy for the large roots you encounter if replanting directly over the same site. Plant the new tree a little high as the site may settle in 2 years.