Bad idea. You wouldn't attempt to pull your own teeth, or take out your own appendix -- so why would you apply caustic chemicals to your own face? Only an experienced professional knows which combination of chemicals will work best on your particular type of skin, how long to leave them on, etc. You could scar yourself for life, trying to save a few bucks. Don't do it.
Microdermabrasion. There is only one, though minor, risk associated with microdermabrasion: tampering with the skin's color balance (in other words, you may get dark or light patches from micro dermabrasion). It's important to remember that pigmentary changes are common complications for other skin rejuvenation techniques, like laser resurfacing, dermal abrasion and chemical peels and scaring if done incorrectly.
Please let me know if there is any way to do a home microdermabrasion or skin-peeling without visiting a dermatologist?
Peeling. I do not know of any microdermabrasion that's a home kit. The microderm requires a good technique and could harm you. THe peel on the other hand can be done at home but the concentration of the agent will be low. Again you can harm yourself with a medical grade peel. THe peels you can get are salicylic acid 2-5% and glycolic acid likely 5-12%. Read more...