Your stones are laminated siltstone and sandstone, worn to smooth curves by erosion on the beach and/or in a river. They contain various small-scale sedimentary structures, but nothing particularly significant.
Yes, the curves and smoothness are almost asking to be caressed.
If you wet them (eg. under a tap), the structures will be much clearer. If you like that, you could achieve a similar, but permanent, appearance by varnishing them carefully.
Some nice finds well done.
I would like to add to Mikes ID with one specimen I recognise, top right in your first image looks to contain 'Ossicles' these are parts of a sea lilly stem.