It depends. Outlets are manufactured so that both sockets are powered from a single source - one hot wire and one neutral wire and a ground wire for safety.
On almost all outlets, those sockets are connected by small tabs of brass that feeds the connections from one socket to the other. If you attach the hot and neutral wires to the screws for one socket, these brass tabs carry that connection to the other socket. It works the same way if you use the press in connections which are holes on the back of some outlets (but many pros and DIYers do not favor using press in connections). The brass tabs on the side carry the power from one socket to the other.
You can change this. If you break off the brass tab on the hot side, the hot wire you attach to one socket does NOT carry over to the other socket within the outlet. This technique is often used to have an outlet with an always live socket (for clocks, etc,) and a switched outlet (for bedside lamps). The outlet is wired with two separate hot leads, one that is always hot and one that goes through a switch. They could be on the same or different breakers depending on several factors. The neutral side may or may not be connected depending on several factors that are not critical here.
You can also separate the sockets if you wanted a dedicated socket for a high draw device, such as a heater, and run a separate line from the panel. (This generally would require a separate neutral).
In your example, if the sockets are set up conventionally, that is powered from a single line, there is no difference, except plugging into a socket is a marginally safer approach than multiple splitters. Be sure that the overall load that is likely to be used at one time does not exceed the capacity of the surge protectors or the circuit breaker on the line.
No it is not safe.
A 15 ampere rated receptacle should not be installed on a circuit protected by a 30 ampere breaker.
You should not be plugging devices that draw more than 15 amperes, into a 15 ampere rated receptacle.
The receptacle in your photo is a 20 ampere receptacle, so you shouldn't have a problem plugging in a 20 ampere device. They make receptacle configurations different, so that you can't plug things into the wrong receptacle. By making a bootleg extension cord, you're bypassing that safety feature.
You're going to burn the place down.
Also note that since the device is active for longer than 3 hours, it would be considered a continuous load. In which case the circuit (overcurrent protection, wiring, and devices) should all be rated for 125% of the load. That would mean the wiring, overcurrent device, and receptacle should be rated to handle at least 22.5 amperes (18 × 1.25). That means a 30 ampere breaker, 10 AWG copper conductors, and a 30 ampere receptacle.
Best Answer
Why you shouldn't use NM cable
NM-B cable (Romex®) is not designed to be used as a flexible cord, and must be properly secured and supported. It's also not rated for use where it may be exposed to physical damage.
Flexible cords have thicker jackets, which are designed to hold up to a bit more abuse. They also contain stranded wires, which hold up to movement much better than solid core wire.
If you were to use NM-B cable in this way, there's a few potential problems.
Abuse
The exposed bit of cable could be damaged, exposing the conductors. This could be a shock, and/or arc-fault hazard.
Movement
Repeated movement of the cable, could cause damage to the core of the wires. This damage could lead to increased resistance, which could be a fire hazard. Ultimately the movement could lead to the conductors breaking, which could pose an arc-fault hazard.
Alternative solutions
Instead you could go with a product like this Recessed Pro Power Kit w/Straight Blade Inlet. The inlet at the bottom of the wall, gives you a place to connect a power cord. The lower inlet is then connected to the upper outlet, using proper cable (e.g nonmetallic sheathed cable NM-B).
This is a much better, safer, and cleaner installation.
You'll also find that surge suppressor receptacles are available, though may not offer the same level of protection as a standalone device.
Products shown are for demonstration purposes only, I do not recommend or endorse these specific product.