Yes you can ... BUT ..... the old varnish was cellulose based, modern "varnishes" are polyurethane based and as such are more harder. It also depends on the on the style and quality of the PVC you wish to adhere to it. To be on the safe side, you can sand the polyurethane to help in adhesion, and if a solvent based adhesive could melt the pvc, .... I would try a waterbased contact adhesive. Apply this product to both surfaces, press them together and immediately pull them apart again, leave until tack free (or nearly dried) and then press them back together again for final adhesion.
Firelighter - Australia
To get hairspray off of varnished wood, use a cotton ball and rubbing alcohol to clean the affected area. Then use a bit of soap and water on the wood, and allow the wood to dry.
Luz
There is always a possibility of getting splinters from a wood floor. You can reduce the probability by having the floor sanded and varnished.
No, it won't stick to most PVC. Oatey's Transition Cement and most epoxies will work IF the PVC is dry.
Yes, wood can be stained then varnished or just varnished. Sand the wood and clean with white spirit, and allow to dry. This removes any dust or grease etc that will spoil the finish. Then first coat of varnish. Give a light sand or rub with steel wool between coats to build up a shine.
Sometimes wood needs to be re varnished or restrained. To remove old varnish, you can use either a paint stripper or sand off the old varnish.
You will need to rough the varnish up with sandpaper then use a bonding primer.
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PVC pipe has less friction. They are also longer lasting than the others.
Woodstain is applied with a rag or brush and then varnished with clear varnish, or tinted varnish can be used, available in different timber colours.
If a wood floor has been properly varnished, it will be waterproof, and you can wash it as you would any other floor. If it is just a matter of removing dust, you could use a Swiffer.