I usually don't answer these type of questions because I feel it is best to learn and play to see what way suits you best. I enjoy coding more in AS3 than in MXML, but I know that I need to use both.

First you don't need to load Flash Professional as Flash Builder is an extremely powerful RIA developing tool. I have used it for years to build various application. If I need an application that deal a lot with timelines, then I switch to Flash Professional, but usually everything I need to do can be done in Flash Builder/Flex.

Secondly, in regards to the language to use. This is what I usually do, most of my coding is done in AS3, this allows me to share specific classes with various different project without needing to manually port them over. If my stage will contain a lot of components that are static, then I usually build a MXML page for that and tie my coding in with AS3. Before I continue, I use Robotlegs for my Framework (per say) which is a pure AS3 framework. Using it anything static that appears on the screen are built using MXML and all the functionality behind it is controlled by AS3.

Some people say that using AS3 you have a better chance of your code running much quicker. It is hard to say, but I do find that everything I need to do in an MXML page can be done using AS3 alone.

So back to your questions, you'll have to find which method suits you, I prefer using AS3 as much as possible and MXML for all static stage display objects (datagrids, buttons, labels, and such). ALL of my functionality is controlled via AS3 and rarely place directly on a stage component. You will have to play around and see what method works best for you. Don't let any programmer drive you into one method over another because of their personal preferences.

AS2 was basically a helper type language which augmented the stage components, however with AS3, it has become far more adaptable and functionality. If you look at the AS3 references you find a number of way to replicate the functions in Flex/Flash. The good part is if is isn't in the reference it doesn't mean it cannot be done. The ability to extend components makes it very versatile. There are thousands of links to people who have figured out simple (sometimes now so simple) way to complete a task in AS3. Just come up with an idea and step through what you want and how to make AS3 work for you.

Not sure what ever I can say about that, play with it until you find a solution that works for you.