Hi Number 1 is more natural..and correct. Number 2 is not natural...and potentially confusing because you are not using the plural form of 'study'. You could say 'He seems to be making little progress in his studies.' I'm interested by what Rick said in the comments about living in London for 2 years and never hearing number 1. I'm British and have definitely said "He doesn’t seem to be making much progress in his studies." about many of my students in the past! :-)

1 is fine. 2 has errors and is unnatural. But as Chris noted, you could say "He seems to be making little progress in his studies." which has a similar meaning and sounds fine. The choice of which to use would depend on the context.

The first sentience is more natural.

Interesting Question. The first sentence is good. If you change the last one to say " he seems to be making little progress in his studies" or "He seems to make little progress in his studies" would be better. To add a little Nuance to discussion read both of my corrections and see if you can tell the difference in meaning between the two. One of them refers to a specific Topic in which they're studying, the other would suggest you are referring to the lack of follow-through or commitment into one's endeavors.

Well, that depends. I'm American, I can see that the 1st sentence is what we'd say in all occasions. However, having lived in London for 2 years now I know that them guys here would never opt 4 the 1st one. Always be mindful of where are you speaking English.