I have been told that depreciation and amortization on rental properties are mandatory. Is it true? Note: I am a non-resident owning rental property in USA.

Not exactly.  However, when you sell, you must pay recapture tax on the depreciation you took or could have taken, so there is every reason to take it when you can.

Also, there may be times when showing a larger income by not claiming depreciation results in a benefit of some kind, such as eligibility for earned income credit or other tax deductions, or to qualify for a loan.  In those cases, not claiming your legitimate expenses is considered tax fraud.

Yes, the Tax Code says it "shall be allowed", which USUALLY means it is mandatory.