Several questions at once and I'll try to answer them one at a time (next time one question per post please)
Several flavors: There are basically two FAST versions - one for SharePoint and one that is the old FAST ESP.
- "FAST Search Server for SharePoint 2010", FS4SP, that's FAST integrated with SharePoint for enterprise scenarios
- "FAST Search Server for Internal Applications", FSIA, that's FAST ESP for internal sites
- "FAST Search Server for Internet Servers", FSIS, that's FAST ESP for internet sites
SKU's. Yes, they are separate SKUS's. AFAIK only FS4SP is available for download on MSDN/TechNet for subscribers.
FAST Search Designer for Microsoft Visual Studio - I've never heard of anything like that.
FAST capabilities. The reasons you specify here is the main reasons to go to FAST compared to SharePoint standard search. Yes you can do a whole lotta fun and customize the FAST pipeline until you bleed. Big difference between FS4SP and ESP is that you are limited in what parts of the FAST pipeline you can modify in FS4SP. Here is one example on MSDN: http://msdn.microsoft.com/en-us/library/ff795797.aspx