Is the adhesive tap strong enough?

It is srong enough to perfectly stick on the surface. But do remember to clean mounting surface before mounting, and stick the light strip with a heat gun especially in cold weather. You can also use the mounting clamp as backup secure.

Is the light strip directly plug-n-play?

For stop turn tail light modes, the 4 Pin trailer connector is compatible for most vehicle's trailer plug, can directly plug in to work. But for some vehicle with auto trailer will only need to hardwire.

Also reverse light wire need to hardwire too.

How to decide light strip mounting direction to make sure turn signal work properly?

Typically, the wire end goes on the driver’s side. But before sticking it in place, it is important to test the strip to make sure the turn signal pattern matches your vehicle, then install once confirmed

Can I use this on my hitch cargo carrier?

Yes. Just make sure the mounting surface on your cargo carrier is large enough to fit the light strip’s dimensions