Below are answers to all your questions.
1. Yes, but I dont see why would you do that. Flex Already have a lot of built in controls and open source libraries for almost every thing.
2. Look at OSMF or may be for starter: [login to view URL]
3. HTML to png, what are you using to render HTML , default HTML control or open source iFrame. Flex/Actionscript provide functionality to export any given of screen to image (PNG/GIF/JPEG/TIF etc).
4. You can use Flash Develop, its open source and free (kinnd of slow than Flash Builder but still works)
5. Never tried that.
6. Can a grid library in Javascript be used in a flex project
you can use iFrame (Open Source Flex Component) to render any kind of libraries . But Why would you do that Flex's own datagrid and advanceddatagrid have a lot better fuctionality compare to many other JS grdis.
7. Same as 6
8. Alive PDF . Have a look here [login to view URL]
9. How to integrate the use of REGEXes and SQLite in Flex Project
Flex support RegEx and have its own processsor. I have used SQl lITE in Adobe Air Project but not in a web projecct so not sure .
10. You can include GSAP in HTML wrapper of Flex app and then use [login to view URL] ("<GSPA Method>",>,"argumment1", "aRG2".............,"ARGn")