1. Since the middle of the 20th c. the nature of war began to change.
2. From the middle of the twentieth century onward the nature of war began to change.
--- Is there any difference in meaning between these two sentences? Does "since" and "from" change anything?
Since the middle of the 20th c. the nature of war began to change. This is incorrect, if you want to use "since" you should write something like this: "Since the middle of the 20th c. the nature of war has changed".
So when I use "Since" I have to use "has/have" and when I use "From" I don't have to do it?
When you are using "since" to say from a certain time onwards you should use the perfect tenses, otherwise use "from.......onwards" or "from X to Y" if you are giving two time references. "From 1750 to 1752" or "From 1750 onwards", for example.