The adjective great has many uses and meanings. But you are correct to use it in the sentence. This use/meaning means "important; highly significant or consequential". So, you are correct. Look at the following link and especially definition number 7. If you click on the Thesaurus, you will see many synonyms (words with a similar meaning). Look at the list with the title "Big League, adjective important" and you will see synonyms such as "critical. crucial, serious, important". These are the words that describe the "problems". God bless the people of the Ukraine.

It's perfectly correct. In fact this is the original meaning of the word. It's related to Dutch "groot" and German "groß". According to Etymonline, the first recorded use of it meaning "excellent" was in 1848: http://www.etymonline.com/index.php?term=great&allowed_in_frame=0 In can sound awkward nowadays to use "great" to mean "big". I think it sounds more natural when talking about abstract concepts than when talking about physical size.

It sounds very strange to me. Usually great is used when you mention something positive.. however as I am not an English native speaker I am not sure whether it is grammatically right or wrong. But I have never heard of it used with negative words though.