If it's lino adhesive, rub it with the solvent recommended on the container. If none is recommended try Goo-Gone first.
acetone and bleach
Goof off will usually remove most self-adhesive glues.
Goo-Gone.
Your linoleum was probably not stained but bleached so there might not be much you can do.
Either use soap & water, or an alcohol-based liquid (such as anticeptic). BOth methods will break-down the adhesive.
Mapei Eco300 is my favorite .
You have to use a floor scraper and scrape it off. It is a grueling job but if you're lucky it might just come off easy.
You can clean sap off of linoleum with regular dish soap. With a solution of dish soap, water, elbow grease, and a scrub brush, you can generally remove the sap from the area. If that doesn't work, try one of the adhesive removers from your local store.
Yes, if the adhesive is smooth, no lumps and if you use a compatible glue, not thinset cement
It allows the adhesive to bond to the vinyl better and also helps cushion
What is under the linoleum? If it is stuck down well, you can put new tiles on there once. However, if you get to "the bottom of things," you may be able to fill in any dips in the floor and correct any other issues that will make your vinyl tiles look even better. It will take elbow grease and a crowbar and some major adhesive remover to take off the linoleum, but it can be done. If you choose to tile over the linoleum, make sure it is super clean and free of any grease.
I have used that to stick lino tiles. It worked very well. Mapei glues are very good.
There are two types of linoleum flooring. For sheet or tiles, you will need a 100 lb. roller, chalk line, adhesive, scissors, staple gun, and steam welder. For the click lock ones, you will need a tapping block, a saw, a hammer, a pry bar, and wedges.
acetone and bleach
You can get adhesive off a table by wiping the table with Orange Glo.
linoleum
You can try a mixture of white vinegar and water to get white water marks off of linoleum. Use a scrub brush with the mixture to clean the area. If that does not work, clean the marks with toothpaste.