Do electric signs need to be listed?

Yes     600.3 Listing.  The National Electric Code requires signs to be listed unless otherwise approved by special permission. The NEC defines special permission as “The written consent of the authority having jurisdiction.”
The Municipalities authority is taken from the National Building code in effect.  The national building code states that signs shall be installed in accordance with NFPA 70.  This is the NEC, National Electrical Code.

What are Installation Instructions, and are they now required on all signs even if they are installed by the manufacturer’s installation crew?

Yes     600.3 Listing.     The National Electric Code as of the 2014 code cycle that all signs require installation instructions.  Installation instructions can be as simple as a one page drawing showing the appropriate fastening and location for connection to the building wiring system.  They can be as elaborate as a complete set of blue prints including foundations, structural steel, sectional mounting and electrical connections required.

Do sign marking and listing labels need to be visible at all times?

No. 600.6 Markings
(D) Visibility. The markings required in 600.4 (A) and listing labels shall not be required to be visible after installation but shall be permanently applied in a location visible during servicing.

See Article 600 of the 2017 National Electric Code page 70-488

Do electric signs need to be grounded?

Yes, with one exception.     600.7 Grounding and Bonding.  The section requires that all signs are required to be connected to the equipment grounding conductor provided at the power source for the building wiring system.  This is the green or bare conductor having zero potential (no energy).  The only exception is 600.7 (B) 1 Bonding. The secondary conductors of a Class 2 power supply need not be bonded beyond the primary connection. This means Class 2 only not low voltage and the equipment grounding conductor must be present where the primary conductors terminate.

Are Class 2 power supplies required to be grounded?

YES. The exemption is from the power supply enclosure to the LEDs. The equipment grounding conductor must be complete from the grid to the enclosure where the line power terminates.

Are there restrictions on selecting the correct Class 2 wire?

YES. Class 2 wire is required to be at least 18 AWG and if your run is over 20’ you will need to
increase the wire size for voltage drop. You also must select the correct wire for the environment whether it is general use CL2 or Plenum rated CL2P or riser locations CL2R. NEC 2017 600.33 will guide you to the correct wire.

See Article 600 of the 2017 National Electric Code pages 70-492-493