First thing: as @ZEKE has suggested in the comments to your question, you should check: How do I determine my games minimum hardware/software requirements? Also, in the end of the day, only experimenting can really give you final answers to that, as @Abstract-Sky has replied in the other answer.
However, you can certainly have some pointers. Here, I will be answering to your original question, the one that brought multiple sub-questions - not to the edited version, because mentioning only "lowest possible environment" becomes just too vague. But, of course, I am only thoroughly answering to part of your sub-questions, because as @zehelvion has well put in the comments, it becomes hard to handle when multiple different stuff is mixed together in the same question.
1) How to determine minimum required DirectX version?
By default, the minimum requirement of UE4 games as of 2014 was DirectX10, because the engine required SM4.0 GPU. So, if you don't use any external libraries or plugins or functions that are specific to DirectX11 or 12, it's very likely that for your game DirectX10 will be also the baseline. So start by checking that.
2) How to check what other dll's I need to include into installer (apart from actuall build)? For example will I need to install VC redistributable packages? If so then which ones? The same goes with directx.
That's impossible to answer without knowing in much more detail what have you used, implemented and included in your game. I think this one deserves a separate question with plenty of details about your game.
3) How to determine minimal windows version? This is limited by directx compatibility right? If my game runs on DirectX10 or higher then all OS versions with at least direct10 will be OK?
Not necessarily. Windows Vista had DirectX10 and still Epic never supported that OS officially. So, it's unclear whether UE4 games would run on that without problems. I've read Epic staff mentioning that UE4 games could work under Vista, but that would be a case for empirical verification in a case-by-base basis. So if you want to aim Vista, there might be some hope.
What is often said to be the minimal system for a game using UE4 is Windows 7 sp1. However, again, if you installed or included any external library or plugins, you will have to double-check that all those also work back to Windows 7 sp1. But if your concern is to go even backward, for Windows XP compatibility, there might be also hope. Epic staff has mentioned in the past (see for instance this forum thread: https://forums.unrealengine.com/showthread.php?1310-Unreal-Engine-4-etc) that they were looking into giving compatibility to a version of OpenGL that would make it work even in Windows XP. In the UE4.2 release, they announced a preview of that compatibility: https://www.unrealengine.com/blog/unreal-engine-42-release
But by default, it's Windows 7 sp1 if nothing external from your game requires Windows 8 or 10.
4) This may seem as stupid question but in which version 64 or 32 bit I should distribute my game? 32 is always better because anybody can run it right?
Well, ultimately that's an opinion based one - therefore hard to answer. But I can give you one of the basic trade-offs: 32bits systems generally can regularly use only up to 2.75 to 3.5Gb of RAM memory, no matter how much total RAM is present in the machine. See this: https://en.wikipedia.org/wiki/3_GB_barrier
So first of all you have to have that in mind. If you consider an OS as memory hungry as the Windows 7 & 8, think of performance and make sure to profile how your game runs under those systems with a 2.75Gb RAM constrain.
Lastly, if you were happy enough to have come to the point of finishing a game for delivery, I think that you should certainly write UE4 for technical details on compatibility. Specially if you are interested in older Windows versions (i.e. XP and Vista).