I will answer a question you are asking and some questions you are not asking but you need to know.
Some objects out of the artboard size
Some objects like the trees are out of the artboard, but as they are part of the objects you have they are showing.
The huge white space to the right is probably used by some transparent objects or the nodes of this objects.
You can try to sellect everithing and put it inside a rectangle of the proportion you need.
I say proportion, not size, becouse if your original artboard is A4 or A3 it has the same proportion of an A1.
The exact steps depends on the aplication you are using, but you can use clipping mask in ilustrator or power clip in Corel Draw.
There is not "normal" size when exporting (not saving) into a raster file (Jpg, psd, tiff, etc.) The output size depends on the resolution you need to print it. Which is a totally diferent matter here, becouse depends on what is your source material, the printing method, final size and viewing distances. You just be carefull on that topic.
Aditional methods to crop your exported file
You can export it as you are doing it right now and crop it after in a raster program. It is an option, but in your case the exported file is a lot bigger than you need it and your file will be too big.
You can "print" your image in a virtual printer. The information is send to a file, not an actual printer. You can shoose the "paper size" for example and the workflow will do the crop for you. The cons of this method is that you can probably loose some colour rpofiles in the process.
Raster or no raster
Depending on the content of your file and the formats within you can send the output file as a raster one or leave it as vector if the case.
That decision depends on many things, out of the scope of the question. But they include original quality and format of the elements, color modes, effects aplied and format asked by the provider.