I think your question is not completed (for the second part of course). I will answer the first part and try to answer the second part as I can imagine.
There is no such “modern” Arabic. There is dialects (which you can name it “modern”)and Formal Arabic. Basically, all the Arabic dialects are formal for most of the vocabulary, but the way of pronouncing is somewhat different and of course the usage of words.
Also, in dialects, you can find some French words in Magharibi dialects. In the Arabian Gulf (KSA, Kuwait, UAE…etc) you can find some Indian and Persian words. And in general of course, you can find English words.
Going between accents in Arabic is quite difficult. But, you can classify dialects to 6 major dialects (the Gulf, Iraq, Shami (which is Syria, Jordan, Palestine, and Lebanon), Egyptian, Sudani, and Magharibi). Going between each major is somewhat easier.