Don't touch me, but please Do!
When drawing an action card as a result of playing an action card you draw it at the end of your turn and thus can't use it that turn. The rules state you discard your played cards after the action resolves, so perhaps this is when you draw the action card. Thinking about this now it doesn't seem like necessarily the best conclusion.
You did make it yourself harder then intended. All text resolves when the card is played,
When drawing an action card as a result of a spoke on the wheel, you draw before taking the action and thus canplay it during your turn.
Actions on a spoke are resolved in reading order. Thus you acted correctly.
I'm really curious about this, as being able to play action cards that let you draw another, and being able to play that card as well would give you quite an advantage in some situations. I'm leaning towards that you can't do this but I just can't seem to find it stated in the rules.
Yes you should try to exploit this Adventage. Take Tyra for example... She does great in just doing that