Homeowner's insurance coverage?

With many policies, foundations are not covered for water damage. With many policies, there's a "buyback" where you can, for extra money (a LOT of extra money) cover damage you have to do to the foundation slab, to go under it to GET TO the pipe.

Sounds like you didn't have that endorsement on your policy.

They will pay for the subsequent damage (possibly up to a sublimit) but they will not pay for the pipes to be fixed. So, they will pay to fix the floor (based on your post, not on any actual assessment of the issue).

The pipes settled at a different rate than the house. As such, there is likely no longer a consistent connnection; which is where the leak occured. You will need to dig up your lawn to address this issue, replace the pipe and return the dirt. Insurance will NOT pay for this, this is considered to be a maintenance issue.

That would be correct unless you have special coverage in the form of a rider that specifically covers water damage from leaks. The rule of thumb is that water coming down is covered, water coming up is not.