Not a verb phrase, though you can turn it into a noun phrase with a gerund "Firstly, improving their eating habits."
The noun phrase examples are grammatically ok but might be a bit short on information, depending on what you're writing and how it's introduced. If you set it up clearly with something like:
"This is due to two main factors: the decline in birth rate, and lack of exercise. Each of these will now be dealt with in turn.
Firstly, the decline in birth rate. This has been a problem since..."
it should be ok. It's difficult to be more helpful without knowing a bit more about what it is you're writing.