Implementation of a singleton HttpClient with generic methods
General remarks

The naming and the design are ok. The only thing that could be improved is the


 HttpClientBase



It's not a base class so you shouldn't call it like this. I suggest HttpClientService.




Timeout = TimeSpan.FromMilliseconds(15000);



Or simply TimeSpan.FromSeconds(15);



Singleton

There are of course mutliple patters for creating a singleton but the one you chose is probably the right one Singleton by Jon Skeet clarification



Concurrency


  I have doubts about its performance or if it would crash on simultaneous calls.


I don't see actually anything that could be further optimized. You call only core APIs that should already do their best.

The methods don't share any data with each other so there is no risk in calling them in parallel.