That step-up cable is not sufficient. It allows for a max amperage of .6A. The TV requires 1A. (12v and 12w usage = 1AMP)

What you need is a power inverter. You would be able to use the wall charger that way. You can also find one with a spare cigarette lighter port to continue using that 5-port charger. Note the 5-port is 50W, and the TV is 12W. You would need a minimum of a 72W inverter. They're not very expensive, in general, but large ones for camping can be.

Also, note the maximum draw on your car cigarette lighter. This is typically 15-20A, but most have a minimum of 10A. At 12V, this would mean a max usage of 120-240W before possibly blowing the fuse. The larger ones out there typically require direct connection to your car battery, or run in reduced power. Running the cable for those larger ones isn't too difficult, especially for camping, but can be a hassle to use while driving.

Having used these regularly for the past 20 years or so...Know that the fans on the small-to-moderate sized ones are...not silent. At their worst, they can sound like a muffled electric razer. They're usually manageable, but if the fan goes bad, it may be time to replace. I usually put them under my seat to minimize this. I tend to prefer ones with cords that plug in, rather than the direct-plug style that clutter the console area.

Check your cigarette lighter, too, for what happens when the car turns off. Can you charge your phone from the cigarette lighter when the car is off? Not all cars can (but some do). If it doesn't, your TV will shut off when you stop for gas. Even if it doesn't, sometimes the draw when your car starts back up will dip power on these enough that they momentarily trip.

With regard to the phone charger, you may be able to find one with enough ports to use wall chargers, or ones that have their own USB ports. If you need one now, you can get them from Walmart, Best Buy, ...you can also usually get them at nearby hardware stores (Home Depot, Lowes, Ace), or auto parts stores (Autozone, NAPA, etc.) I'll give some Amazon examples:

3 outlet, 2 USB, and extra 12V port, 150W max.

Here's a smaller one, 1 outlet, 1 USB and an extra 12V port, 100W - although this one you can't put under your seat - it plugs directly in.