There is a product, usually sold by the gallon at pool supply stores that could work for you. Best bet is to avoid the oil. Your filter will pay the price by having to be specially cleaned and or replaced.
Oil gets in a swimming pool because someone grabbed a bucket of oil and threw it in the pool.
Yes. It clogs the filters. Badly.
No
painting of oil is called oil paint and painting of vinyl is called vinyl paint
you can if you want to it won't hurt the tan is on your skin and will stay there if you go to the tanning salon regularly :)
Pool with a vinyl liner.
Tanning oil should not be used when using a tanning bed. Aside from the damage you may do to the equipment, the oil will increase the damage done to your skin and doesn't provide SPF protection.
You can't ... since the above ground pool is made of vinyl material, you need to apply a vinyl patch. Has to be a like material to be compatible.
Get
Vinyl Liner
One of the biggest fears that most pool owners have when it comes to their vinyl pool liner is discovering a rip or a tear in it. The fortunate thing about holes in vinyl liners is that they are very easy to repair. http://www.pondpro2000.com/epdm-pond-liner.html
Tanning oil You can buy this at your local chemist or super market