Above points are correct and I want to add some more important points about Static keyword.
Internally what happening when you are using static keyword is it will store in permanent memory(that is in heap memory),we know that there are two types of memory they are stack memory(temporary memory) and heap memory(permanent memory),so if you are not using static key word then will store in temporary memory that is in stack memory(or you can call it as volatile memory).
so you will get a doubt that what is the use of this right???
example: static int a=10;(1 program)
just now I told if you use static keyword for variables or for method it will store in permanent memory right.
so I declared same variable with keyword static in other program with different value.
example: static int a=20;(2 program)
the variable 'a' is stored in heap memory by program 1.the same static variable 'a' is found in program 2 at that time it won`t create once again 'a' variable in heap memory instead of that it just replace value of a from 10 to 20.
In general it will create once again variable 'a' in stack memory(temporary memory) if you won`t declare 'a' as static variable.
overall i can say that,if we use static keyword
1.we can save memory
2.we can avoid duplicates
3.No need of creating object in-order to access static variable with the help of class name you can access it.