'Suppose I have set up the system with front speakers “small”, crossover at 80 Hz and the crossover on the sub at max frequency, a quite normal setup.'
If you have the 'sub yes' option on, then the receiver will use a crossover and send the bass to the subwoofer.
'And also the complete signal is fed to the sub, meaning the crossover frequency at the sub is now determining the split? But since it is set at max (=120 Hz) there will be an overdose of bass since part of the spectrum is now coming from the fronts as well as the sub .'
The receiver will only send bass at the crossover you selected, that is with some kind of roll-off for the bass of the main speakers, with the sub then taking over entirely below 80 Hz. This won't be the case if the main speakers are set to 'large', then they'll get all the bass and so will the subwoofer.
The crossover setting on the sub is really there for if you don't have a receiver that has a crossover control, like a non-home theatre stereo amplifier. When you set the crossover to maximum on a receiver using a crossover, I think it just has the effect of bypassing the subwoofer's crossover. You don't need to use two crossovers to do the same thing.
'This is also what I seem to hear … more bass … although it is only the part between let’s say 120 Hz (start of sub kicking in) and 40 Hz (lowest freq of fronts) which gets 3 dB extra, it is not always easy to distinguish.'
If you have the sub turned off in the pure direct mode, then the amount of low bass depends on your main speakers and there room position. With it turned on, you should get very similar bass performance as you would get in the non-pure direct modes, unless you've adjusted the tone controls.
My view is that 'Direct/Pure Direct' modes are there more for specification listings. This allows the manufacturer to avoid giving info on the performance of the tone controls, Dolby Digital decoding performance, DTS performance etc. Amps and equipment made for the high-end market are usually more willing to provide comprehensive specifications. All this stuff about 'ultra-clean analogue pure direct modes, 96 kHz/24 bit etc..' is really just a case of marketing to audiophiles worried about tone control drift. Bypassing the tone controls will probably have a measurable objective effect, ie. maybe the signal to noise ratio will be slightly improved, but this change will probably be entirely inaudible if the tone controls are set to flat. Bypassing of the subwoofer in pure direct does make some sense if the subwoofer is poorly integrated with your mains. This maybe more noticeable on two channel stereo music than with film soundtracks.