Where do you hear the glitches, speakers or headphones?

Can you try the PC in another house with different electrification or the RME card in another computer // in another loction ?

Where is this beep from ??? Maybe a faulty project / vst ?

What happens if you use the interface for simple audio playback ?
Use i.e. MusicBee player, which supports ASIO driver, to playback a mp3 or flac file.

What happens if you use a fresh DAW project with no plugins.
Use the RME ASIO driver.
Use only one input and the main out where the nearfield monitors are connected through.

Save the settings of Totalmix and eventually also reset TotalMix FX:
TM -> Options -> Reset Mix -> Total Reset.

If the noise also happens when you don't use the HDSPe at all (no audio software running) then the source likely is the computer (components). What happens is that the ground lines are polluted with computer noise by various load states. Especially graphic-cards induce lots of this, but also USB (mouse movement). The base frequencies depend on the source (USB frequency, GPU frame-rate), a 125 Hz mouse will sound different than a 1000 Hz mouse, for example. The level of the noise usually depends on the load of the component responsible (higher GPU load at same frame-rate increases noise levels). And then there are modulation effects that alter the sound of the noise, if the sound keeps altering then it's often easier to discern.

Where the speakers are concerned this is ground-loop related. If you break pin 1/shield on (one side of) the XLR cables to the speakers the noise should be gone. There are (overpriced) adapters available for this, but you can just literally cut the wire of pin 1 (usually on the speaker's side of the cable). Using an optical digital connection in between also helps, if you have the means to do so.

One thing to know about is that there are several ground-loops in effect at the same time, which leads to combing effects. Especially the connection between graphic-card and display can have much of an effects. Try disconnecting everything but the bare necessities from the computer, then change the power-plugs around on your power-strips. Try display, speakers and computer on the same power-strip and also try changing one or two into a different power-strip. The run-times of the different ground-noise signals (loops) can change by this and thus you may get cancellations that lowers the noise-floor.

Sometimes external synthesizers connected to the system can be a problem, depending on their power-supply. On Gearslutz one guy had problems with two out of four synths, a DI box with ground-lift helped there.

Where the headphones we first have to make sure that the speakers can be cleaned up when you break the ground connection before we can look at the headphones. It's strange that the headphones would sound like cracks, though. Are you sure that this isn't a problem of audio buffers or PCI slots being used? Does that happen with all buffer sizes?

Where did you lift the ground? This part was only about connecting external equipment. For the speakers you need to break pin 1/shield on the cable to the amp/powered speakers, there is no way around it (other than going optical in between).

The graphic-card creates the noise on its ground line, which then travels over all ground lines on the computer, including the AIO and everything connected. Inside the powered speakers ground is connected to earth, which then forms a loop with the earth line of the computer power-supply, which is connected to computer grounds. Same for the GPU + display and possibly other external stuff.

Breaking pin 1/shield breaks the line over which said noise travels towards earth and thus breaks the loop that is affecting the speakers.

Although it looks the be the graphics card, it can also be the cpu throttling you are hearing. If you know how , try to disable speedstepping and all C states (C1 C1e etc in the bios, mostly under CPU advanced). This is something you want to disable anyway on a DAW.