You will have to extract the server and common zip files under Mods/BF2 just like you did for FS. Then you have to move the textures you want into your FS mod in order to see them when you test the map. From previous posts the BF textures are frowned upon.

It is pretty difficult to use the existing textures and create a fresh look. Creation of new textures would be a better idea rather than using old BF ones.

But, BF2 has a lot of files so if you extract them all the editor takes alot longer to load as it will read all the BF files when opening the FS mod.

You can use the color textures, not the details ones. You cannot use BF2 overgrowth, you can use 2142 textures and vegetation though.

"Munchkin: One who, on being told that this is a game about politics and intrigue in 17th century Italy, asks to play a ninja."
— Andrew Rilstone

Yeah, you can use 2142 detail textures instead.  And you can use 2142 Overgrowth.  You are not allowed by EAs rules to use BF2 content in a 2142 mod.. hence you can't use the detail textures and overgrowth (undergrowth and color textures are stamped onto files so you can use them because there really is no way of knowing if they came from BF2 or 2142)