Yes, if the installation involves a (1) communication circuit or class 2 signaling circuit over 30 volts or under 30 volts but more than 100 va, (2) amplifier circuits not using class 2 or 3 wiring, or (3) any circuit operating over 15 volts that control, generate, transmit, transform, or utilize more than 25 watts or va. See section 93.0202 for more details.

A permit is not required for any type of fence under 3'6" in height.

A permit is required for a masonry or concrete fence over 3'6" in height, and for a fence of any other material over 10'0" in height. 

Please note that even though a permit may not be required, all fences must comply with the requirements of the LA Zoning Code.

No, when done as part of the City's "Water Conservation Retrofit Program" pursuant to the City's Water Conservation regulations. 

However, a non owner-occupied single family dwelling requires a permit obtained by a licensed plumbing contractor.