Need a little help.

1) I can't launch Heroes of Might and Magic III HD Edition.

This is quite vague information. It's unclear which version of Heroes the mod is being launched with, and in general... It's better to communicate via ICQ.

2) I really need to extract a monster (a fanatic from a Castle) from the game, leave only the "bow" animation for it, recolor it to white, and convert it into a 165x165 pixel GIF.

In the DefPreview program, you can see the entire storyboard for all animations. There isn't a "bow" animation specifically (there is "move forward," "death," etc.).
The algorithm is roughly as follows: In DefPreview, perform the action "Unpack everything for DefTool." You will have all the frames in BMP format. Select the set of frames you need for your animation. Then, make the background transparent, which requires converting the BMP to PNG or JPEG in a graphics editor while simultaneously changing the image size. And then, use some kind of GIF animation program to compile your frames, like that fire elemental.
The H3DefTool program is designed for creating and editing def files and works with the list in HDL format, which is created by the DefPreview program.
In general, there is a lot of information about Heroes and modding on specialized websites.
DF2 :: FORUMS -> Heroes of Might & Magic III
Guild of Artists of Might and Magic
This is from there :)
Battle of the Bone Dragon with a Monk


And this is just a cute picture of an Ice Elemental



and a Troglodyte


(I just found them)