You will gradually earn “favor” with your Guardian (10 every twelve Eorzea hours up to a maximum of 1000). When this has reached a certain amount, you can petition the god or goddess to bless you with a temporary boost to the development rate of various skills.
It seems they need to fix this in-game. You're supposed to get 10 every 12 Eorzea hours
, however long an Eorzea hour is. This would make the max 1000 points make sense.
The Anima limit makes sense. For casual players they will be able to get around easily. The more hardcore players will just have to learn that, if they want to play longer, they will have to walk. Later there will probably be other forms of transport as well (chocobo, airship, ferry, etc). Until then, use it in moderation.