Rainbow gems -- finite or infite for F2P players?

Apologies if this is a stupid question, but I just started playing the game 2-3 days ago.

If I want to remain a F2P player, will I eventually run out of rainbow gems that the game's storyline gives out? Or are they also given out (at a reasonable rate) during events and such?

you get each day one gem, the story line gives after some stages one (if you win the first time) and you can get one gem from the fortnight islands (but only if you are able to win the 30 stam island)

I recommend you to save you gems, the best time to get some rare recuits is during a Sugo fest, I think the next will be in about 30 days (my personal rating)
The other things they are worth to spend gems are turtle time and Raid bosses (but they are really difficult, I think you will need some time before you are able to defeat them...)

Thanks MASI!