Legal Question in Real Estate Law in California

Taking the questions one at a time:

Yes, it is legal for your neighbor to look over your privacy fence. Privacy rights tend to become violated, if at all, when the snooper misuses information he or she gains, or seriously interferes with your use and enjoyment of the property. Merely looking over a fence is nowhere near enough to trigger an actionable privacy-rights violation.

An HOA inspector acting in an official capacity probably has an implied right to trespass on your property and look over your fence to see, for example, whether you are keeping hogs or have more dogs than HOA rules allow, or are growing marijuana. If the "inspector" is not carrying out a legitimate HOA interest, coming on your property to peek over your fence is probably a trespass for which you could sue and receive nominal damages (say, $1) and maybe get an injunction forbidding that person from entering your property. Maybe.

You have privacy rights, but neighbors also have a right to look 360 degrees and to look over the fences that separate their land from the land of another. Indeed, fences over ten feet tall are presumptively illegal spite fences in California.

The "view" portion of your fence must be facing another property. The world is round and every parcel of real estate has another parcel of real estate next to it everywhere, even oceanfront or international boudary parcels.

There are limits on snooping and trespass, but on the other hand we live in a society where no one has an absolute right to supreme isolation, and there are many implied invitees who can enter your property for various reasons and in the process may observe conditions that don't look proper and make reports. These include the letter carrier, the meter readers, the HOA inspector, the UPS delivery driver, the neighbors, the city building inspector, the trash collectors, and on and on.