MySQL server and iOS

I run a site write now with a quite big MySQL database. Now, I want to create an app. I will need to use obviously a database de to the fact my data are already there.

Thus,

1) Should I keep using the MySQL server and my iOS app will connect to this MySQL serve for getting data?

2) is there any problem if I use the MySQL server ? Security issues maybe?

3) if I have to change the MySQL server, what database infrastructure I need to build and work with?

I am totally newbie on iOS apps. And now I planning to face any issues my iOS app will have.