No, auto transformers do not provide any isolation between primary and secondary circuits since they utilize a single winding. Isolation is an important safety feature provided by conventional two-winding transformers.

The three common voltage regulation methods used in auto transformers are - tap switching, coupled transformers, and zig-zag connection of windings. However, these are complex compared to neutral tapping used in isolation transformers.

No, the single winding of an auto transformer must be wound over a magnetic core made of ferromagnetic material like silicon steel for it to operate properly based on electromagnetic induction. The core provides the magnetic path necessary.

Yes, due to the direct connection between primary and secondary circuits internally, there exists a finite possibility of electric shock if safety precautions are not followed in auto transformers. Isolation transformers are safer in this regard.

In general, auto transformers are marginally more efficient than an equivalently rated isolation transformer since they use fewer conducting materials (only one winding) leading to lower I2R copper losses. the efficiency tends to be 3-5% higher for an auto transformer.