How can I create "drop caps" Anchored frames tool: "Run into Paragraph" in a text document, and at the same time be able to feather the text to the bottom of the pages? I´m using FrameMaker 10.

Presumably you are doing the DC as a single letter inside an Anchored Frame run-in from left.

Back when FM had a manual, this was the method discussed in the manual. The manual, however, also said "Framemaker does not feather text in a text frame in which text runs around graphics."

That was FM7.0. I don't know if FM has enhanced DC or feathering since then.

If I had the requirement, I might look at putting the whole lead paragraph in a borderless table.