> I was wondering which is the best solution for connecting an external stereo buss compressor with the UFX

This is how to configure external HW for mixing "out of the box" in Cubase:
https://www.youtube.com/watch?v=H-N-9AGlrXk

> Also I would like to know is there a preferable connection for a guitar processor (Axe Fx III) and the PC?
Basically its a good strategy to avoid any unnecessary AD/DA conversion.
But most external devices, like the old Kempers, are unable to get the clock from the recording devices, which is not so nice.
In such cases I would tend to record analog then to avoid making this gear to clock master in my setup.

> Is the traditional Guitar->Axe FxIII (balanced to TRS) ->Ufx->Daw signal chain the best?
Yes. But what you could also try is to connect the Guitar to the Instr input of the front of the UFX
and then to use one of the analog outputs to bring the signal to the Effect processors guitar input.
Then you can use i.e. DURec to record the signal directly coming from the Guitar.
You could playback in a later step from DURec recording and perform re-amping.
i.e. to try other virtual amp and effect settings.
Also very useful if you want to use DURec as tape deck for quickly recording ideas.
Its much quicker this way compared having to boot the PC, starting the DAW and setting up a project to record your idea.

I am currently using my UFX+, which is comparebale to your UFX, this way:
- connect guitar to Instr 9
- Single coil guitars I connect to Instr 10 (+3 dB extra gain to compensate lower output of single coils)

This Guitar Input signal I send via UFX+ Analog Out to Distortion Pedal and then to my Marshall combo.

Now I am building a parallel Effect Loop for my Marshall to keep the sound tight even when using two Multi effects.
I connect Amps "Effect Send" to the UFX Analog In.
This signal I route to the two Multi Effects also connected to the UFX+.
I need to configure kill-dry on both Multi-Effects to get no unwanted phase shifting effects.
Now comes the magic trick which retains the punch of the preamp signal
I send the unmodified signal directly out to another output to the amps "Effect Return"
plus additionally the 100% wet signal of both multieffects.

The sound I am recording then with 2 mics at the amp.

I am recording most of the times with DURec
- direct input signal
- two mics with the final amp signal
- the backing track

Recording the pure Guitar signal even enables me to use virtual Amps in the DAW ...

OK, this is not exactly what you are going to do ... I only wanted to tell you, that it really works.
And by this "parallel effect loop" sponsored by RME UFX+ I have a well defined punchy / not muddy sound.

I can use the UFX+
- to compensate the lower output of single coil guitars without having to change Effect levels or the volume of the amp
- as Tape deck (DURec)
- for reamping using other effects (DURec)
- find the proper Mic position
- use TM FX Phase button for 180° change to ideally position the two Mics
- make sound quality better by building a parallel loop

So, with the UFX don't be shy to even use the Instr Inputs for plugging the guitar