No. Once your visitor turns to a customer they are excluded from the remarketing list and therefore will not be targeted anymore.
Every store is unique with different products, prices and visitors. Sometimes, the visitor might click on the ad and make a purchase immediately. Sometimes, they just need more time for decisions. We always recommend to be patient. If you are uncertain whether the app measures conversions, always ask us.
We always recommend to ask about the optimization after a longer period of time, so AdWords has a lot of data to judge from. As far as the setting of the dynamic remarketing ads as from Google, there is not much space for the campaign optimization. You can have a look on your own web and take a visitor's journey. Is it easy to navigate on your web, edit cart or make a safe purchase? You can also try to experiment with different bid values but these are, in general, more advanced features.
You can always ask us, whether it is possible to optimize your campaigns.
Once you choose an AdWords account you have to stick to it. Changing accounts on the go is possible, but it requires reinstall of the app and connection to a new account where, of course, all the performance data would need to be build up again.