Removing linoleum from hardwood can be done but it's very hard. It involves a lot of scraping and sanding. And to boot, if the linoleum is pre-1980s, then it most likely contains asbestos. Sanding it means running the risk of inhaling a cancerous material. You can buy a respirator for this job for under $30, along with a change of filters. It would be nice. You can consider doing the removal yourself and contracting out the 'sanding/finishing' part. DO tell the contractor that you removed linoleum so he knows to wear the proper respirator. (A plain dust mask is hazardous.)
To test your glue & tiles, look in the YELLOW PAGES under ASBESTOS ABATEMENT & REMOVAL SERVICES for companies. If none of the 'listings' do the test, ask them if they know. At worst, contact a local Municipal Inspector or County Health Department for leads. It's $$$ well-spent to find out you do, or DON'T, have to worry about the glue and tiles.