You can't really make a swinging gate using unmodified Quake; your best bet is to develop for a mod like progs_dump, Alkaline, or Arcane Dimensions.

progs_dump would be the most straightforward to use if you haven't done much Quake mapping before, and it does add a bunch of rotation-related entities as you can see in its manual (there's a "Rotation Entities" section near the end). As well as a bunch of other tools and helpful things you may want.

There's a progs_dump thread with a download link and some discussion over here: https://www.celephais.net/board/view_thread.php?id=62207

If you're going to develop for a mod like progs_dump, then in general you'll need to figure out how to configure TrenchBroom to target that mod, how to launch Quake to run your mod, etc. I think the progs_dump manual has some good info about how to set things up, also there's an (older) video about that here: https://youtu.be/_zM2j7RWz2w?si=hbzzUEn0I7UzdRk6

BTW I know on reddit some folks suggested you hit up the Quake Mapping Discord for live help, and that's a good idea for when you run into problems/questions. 

Every time setting "func_detail" to new brush(es) I need to add a key "_phong" and set a value "1".
Is there any way to set it as default and newly assigned func_detail brush obtain this key automatically?
Thank you. 

You need to edit the .FGD file 

(I`m using ad_1_8.fgd by Sock) but need to know what exactly to do. There is no entities with predefined keys in it(?) that should be an example. There`s any tutorial for editing/creating entities definitions file? 

Ah, I thought you were using one of the basic FGDs so you were missing the key entirely. Looking at ad_1_8.fgd, it has the following definition for func_detail:

//_____DETAIL_____
@SolidClass base(FuncLighting) = func_detail : "...

meaning that func_detail should take all the keys and values that are defined in FuncLighting group/class, which is defined earlier in the file:

//_____baseclass for BModel lighting options_____
@baseclass = FuncLighting [ ...

and this group/class has the following key defined, among many others:

_phong(choices) : "Phong Shading" : : "1 enables...

So with that .FGD, any func_detail brush should have tons of keys defined in FuncLighting appear in the Entity window in TB.

Or the issue is that you actually see the "_phong" key but it's a hassle to manually select "1 / Enabled" for every func_detail brush?

Then try setting a default value like so in FGD (added 1 (or try "1"), between two colons which have nothing between them in original file):

_phong(choices) : "Phong Shading" : 1 : "1 enables...

But it probably won't work the way you want - if I remember correctly TB won't include the key/value pair of an entity in the .MAP file unless it was manually set, I think. So it seems like these default values are there just for information. 

Thank you for such a detailed answer! Really, ad_1_8.fgd by Dan Ellis & Bal & other has more keys already available in entities options window unlike Sock`s ad_1_8.def, wich I use. Editing .fgd does not give me the expected result so I probably just will use .fgd instead of .def