Re: Basement Piers / Supports
It seems as though you have some structure support issues ..... and no they shouldn't be just sitting on the floor. Besides it looks as though there is issues with the floor as well.... whether it's soil , water heaving or just poor concrete it's difficult to tell.
The steel adjustable columns are an acceptable system .... but ... it also depends on your local building codes as to what is allowable.
Whatever type of support columns use will require a concrete footing under each one.
I strongly recommend you contact a structural or civil engineer to appraise the situation. They will be able to advise you as to the appropriate type of supports , where , how many. They can also provide you with a certified drawing including the dimensions of the concrete footings for the supports.
As for the water issues you should consider a foundation contractor to evaluate the situation. It's unclear as to what the foundation is comprised of so it's difficult to suggest a course to follow.
You may end up digging the exterior around the entire perimeter and applying a waterproofing system to the foundation and installing a perimeter drain sytem along with a sump pit with pump.
Hopefully this helps.
"" an ounce of perception -- a pound of obscure "