Screws will rust depending on the material they are made of and the environment they are in.

Different heads are often used for aesthetic purposes. Flat heads sit flush, oval heads, pan heads, hex heads, and other heads sit externally. 

Screws have built up pressure when installed, over time this pressure can cause them to loosen along with many other factors including vibration and material expansion or contraction.

Plating can act as a protective coating and a sacrificial barrier to protect the steel / metal underneath from rusting.

Some screws are and some are not it depends on the material they are made of. Usually it is just the head that is magnetic.  

A washer head screw is a screw with a wide head that looks like it has an inbuilt washer. It provides unique benefits over traditional screws. Their design enhances grip strength, reduces surface damage, and ensures a secure fit.  

Most machine screws are usually designed to hold together parts of electronics, engines and industrial equipment. For this reason, they are typically much stronger compared to other types of fasteners

Neither! Screws and nails are both great for different tasks. One or the other will be better depending on the application.

During fastener tightening, as pressure builds between the contacting and sliding, thread surfaces, protective oxides are broken, possibly wiped off, and interface metal high points shear or lock together. This cumulative clogging-shearing-locking action causes increasing adhesion. In the extreme, galling leads to seizing - the actual freezing together of the threads. If tightening is continued, the fastener can be twisted off or its threads ripped out.

If galling is occurring than because of high friction the torque will not be converted into bolt preload. The change may be due to the surface roughness changing on the threads or other similar minor change.