[member="Taeli Raaf"]
Although it feels like a cop-out, I invariably have to say "it's a game". As with our movie writers, the intent is on crafting a story that looks good to an audience with a short attention span, so the complexities of ideology tend to be ignored in favour of whether it's interesting or not. Most of the Star Wars games have never bothered to dig into the complex nature of Sith ideology: they frankly find it easier to go with 'Sith are evil', and use that to do just about anything that fits that template.
That said, impersonating a Jedi while practising as a Sith is perfectly possible: Palpatine was able to conceal his presence in the Force from the most powerful Jedi Masters of that era, while Darth Zannah (Bane's apprentice) infiltrated the Jedi Temple as a Jedi in order to access their Archives. There are certain skills that enable a Dark Side user to conceal their presence, and Zannah was a Sith Sorceress, so she could easily craft a glamour that gave the illusion of being a Light Sider.
As for using 'Jedi abilities', you honestly wouldn't need to: even in the movies, we've never seen a Jedi technique, one that uses the Light Side (that I can recall off the top of my head). We've seen Telekinesis, Force Sense, Force Jump, Mind Trick: these are all neutral skills, available to users of either side, none of the, requiring the Light, merely the ability to manipulate the Force. If you needed to use Force Healing, for example, then yes, their cover would have been blown: that requires passivity and for the Force to work through you, which no Sith could ever do. So if a Sith honestly only ever used neutral techniques, they might never be detected as Sith.