Yes & No! While washing regularly is important but without protection it exposes your vehicle to unwanted contaminants. These contaminants will damage your paint over time. With protection on your vehicle, the wash process is much easier. 

Wax layer is suppose to last up to 3 months, if the vehicle is washed regularly and with proper wash technique. It also depends on what your vehicle is exposed to.

Claying is the process of removing embedded surface contamination. Please read our blog post for in depth explanation. 

http://www.shieldandsheen.com/decon-clay/

Unfortunately no. Clay only removes above surface contaminations and scratches are below surface. Scratches are basically missing clear coat/paint. 

In auto detailing scratches have different names depending their severity. Regardless of severity, scratches appear when the smooth clear of your vehicle has been removed. Scratches appear due various reason such as improper washing and drying technique, dry rubbing your paint without lubrication, touching/rubbing against dirty vehicle (you may rub the dirty into the paint), Automatic car washes that are not properly maintained,  car accidents and more.

In a perfect world your vehicle should be washed weekly