Hi Boac,
Firstly - could the slab you want to fix to be moved ? If it can - mark out the holes drill through and lift it - place the bolts through the holes so the heads will underneath the slab and reset.
You can buy proprietory anchors - Ramset - is one make, you drill a hole, push in the anchor and set it by knocking its internal wedge down. To use these devices you'll either need the slab to be quite thick or good concrete underneath.
Stainless steel should not rust at all but you may have trouble finding stainless bolts or studding - I wouldn't use Nylon to fix anything on the heavy side.
Hope this helps.