The Far Wilds tries to make sure you are always able to increase your domain level. It does this by sometimes changing the next card you would draw. Autodraw works any time you draw a card (start of game, start of round, card draw as effect from played card).
2) If you don't have a Base in play or in your hand, you will draw the first one available (closest to top of your Deck) from your Army if you have the domain to play it.
3) If you have a card in hand that you don't have the domain for and you don't have a card that gives you that domain in hand that you can play, you will draw the first available card from your Army that gives you that domain if you have one. If there isn't a card in your Army then you will draw one from your External Card list.
4) If you don't have a domain providing card in hand that you have the domain to play, you will draw the first domain providing card in your deck.
This means that if you start with one Grove in your Army and later it is destroyed. You will keep drawing Groves as long as you need them.