Can I work at a place where I pull parts, drop engines, hang engines which get sold back into the aircraft market? Am I allowed to do so without a A&P License? I've been told that it is legal if you're supervised. If so what is considered supervision? I live in California with no aircraft schooling at all if that matters.
Anyone can work on a plane. Only an A&P can certify the work and return the airplane to service, with a few exceptions. A plane cannot (legally) fly unless the work has been signed off by an A&P, with a few exceptions found in pt43 Appendix A Para C (preventive maintenance). Even if the work is allowed by pt43 App A Para C, the person performing the maintenance must be at least a private pilot, the airplane must belong to (or be operated by) that pilot, and the airplane cannot be in commercial service.
"Supervision" is loosely defined and is up to the A&P to decide in the field. The idea is that the supervising mechanic should be observing while you work but the language allows the mechanic to determine exactly what must be observed while work is being performed. Some will want to be over your shoulder the whole time, some will trust your word, but most are somewhere in the middle (trust but verify).
You may work in a shop as an apprentice and do all of the work you describe but you will be subject to the directions of your supervising mechanic. Your time as an apprentice counts toward A&P certification, too. They will likely start you at very low pay and assign menial tasks until you prove yourself to be reliable. Sweep the floors with a smile and don't be offended that they don't throw cylinder replacements at you on day one. You need to build up trust before shops will let you do any fun work on customers' airplanes that can easily exceed the price of most middle class homes.
You can, but on a certified aircraft, you will need your work reviewed and approved by a licensed A&P which will be documented as such in the airframe, powerplant, or propeller logbooks.
On the other hand if you own an amateur built, experimental category aircraft which you completed at least 51% of the construction on, you are allowed to do your own maintenance on that aircraft without A&P signoff. A&P and Repairman can sign of conditional on experimental. Anyone can work on experimental.