New Rules take effect immediately. Your turn is over after you have completed all the required rules and you have chosen not to perform any optional actions.
The Online FAQ and the rules both tell you that new rules take effect immediately (I didn't quote the rules pdf, but look under New Rule:, and also gives blue example boxes)
Q: Suppose the rule is Play 2 and for my second play I change the rules to Play 3. Do I play one more card or am I done because I played 2?
A: All rules take effect immediately, so you would need to play 1 more card because the rules at that point had become Play 3.
The turn order is described in the rules
On Your Turn:
1) Draw the number of cards currently required.
2) Play the number of cards currently required.
3) Discard down to the current Hand Limit (if any).
4) Comply with the current Keeper limit (if any).
Optional actions allowed by New Rules, Keepers, etc may be performed at any point during this sequence.
So for example, Recycling is an optional rule that says,
Once per turn, you may discard a Keeper you have on the table and Draw 3 extra cards.
You can choose to use its ability anytime during your turn sequence.