Yes! Of course! Since you are inside the FIR and in controlled airspace. ATC service is provided, but you must avoid entering that country’s airspace.
It would be quite useful indeed! There are however a few websites where one can check for dangerous flying zones around the globe. There are other areas that although not restricted in any way, are considered by other countries as unsafe (war and conflict zones for instance). Safe Airspace is one of such websites and the one I use myself when planning on Simbrief.
Many airlines, especially European ones, use EASA’s official Conflict Zone Information Bulletin. Most info on both sites is the same, but I prefer Safe Airspace myself. All this to say that many airlines use 3rd party websites for gathering such information as opposed to having such info clearly visible on their planning map.