In Final Fantasy VII, is it possible to get Lvl. 4 limit breaks without unlocking the lower levels?
Yes and No you can unlock level 4 without fully unlocking all your limit breaks. For most characters (with the exception of Vincent and Cait Sith) there are 7 limit breaks. The first level in levels 1 to 3 are unlocked by how many enemies you have killed with that character.
For example take a look at Clouds table to gain limits from GameFaqs
If you have 120 kills you will learn Limit 2/1, without ever using your limit break with cloud you will unlock level 1/2. If once again you make 200 kills with Cloud with out ever using 2/1 you will unlock 3/1. Now to learn Level 4/1 you would need to get 3/2, but it is possible to never learn 1/2 or 2/2 limit breaks.
Not according to this information I've found:
It appears the L4 limit breaks require you to have all previous limits.