How to solidify melted chocolate?
I am scared that the chocolate will stick to the counter top (in plastic) or the sheet pan. 


Don't do it on the counter top. The best surface would be a silicone mat from a baking store - a smooth one, not the ones that seal an woven steel wool inside and so have a relief pattern. If you don't (yet) have that, plastic foil will do, you'll be able to peel it from the chocolate when cooled. 


  I am scared that it won't fully solidify. I am wondering whether the counter top should be cooled down (which is impossible in my kitchen). 


20 C is a good temperature for cooling chocolate. Never cool the counter top. If anything, it would be best to warm it slightly so the bottom of the chocolate bark is cooled slower than its top, this gives the best shine. You can skip that though, it's a perfectionist's thing. If you are interested in a deeper explanation, see How to prevent &quot;sweating&quot; chocolate covered strawberries?. 


  I am scared that it could be hard to warm up the chocolate at a high enough temperature without burning it so that it is easy to spread smoothly.


Here comes the most important part. The problem is not even burning, the problem is distempering. The chocolate will melt at around 30 Celsius, but will distemper at around 33 Celsius. Distempered chocolate solidifies in a grainy mass. You should not let it go warmer than 33 C, better yet 32, and that's a very narrow temperature range to hit. 

To avoid this, you have to work in small batches1, use a double boiler for warming up, and use a candy thermometer. Don't use the microwave, that's uncontrollable and only useful if you are going to make some kind of chocolate mixture, not if you want to resolidify it as bars or similar. Also see What is the best way to melt chocolate? and What is the purpose of tempering chocolate?. 

1 At the beginning, "small" means "so little you can stomach tossing it" because you will probably get it wrong a few times, it is a skill you have to build. But not so little that it smears onto the bowl and cannot be handled, I'd say the minimum is somewhere between 25 and 50 g if you are using a small enough bowl. Later, when you are confident in your process, "small" means "as much that you don't get a heat gradient in the melted chocolate in the double boiler", it depends somewhat on geometry and bowl material, and you have to experiment with that a bit to find out what amount works well.