We need to clarify our terminology here: if you're talking about a stereo amplifier, then there won't be any HDMI inputs and/or outputs, and so the question is academic. Or indeed pointless.
If we're talking about a home cinema receiver or amplifier, ie with surround sound processing and able to drive five or seven speakers and a subwoofer, then yes most of these now have HDMI inputs and outputs, so can take the picture from multiple sources and route it to the TV. All but the most basic HDMI-equipped receivers can also extract sound from the HDMI connection.
So...
1) If you're using a stereo amp, there won't be any HDMI connections, as already discussed. I'd run analogue audio outputs from the recordable DVD machine and the Humax to the amp, and also analogue stereo from the TV if you want to watch broadcast TV from the TV's internal tuner with sound via the amplifier. If, of course, the TV has analogue outputs.
2) If you have an AV receiver able to take sound from HDMI inputs, use those for the DVD-R machine and Humax, connect an HDMI from the receiver's output to the TV to allow the video to be sent on to the telly, and run either an optical digital connection or stereo analogue connection from whatever audio out the TV has back to the receiver so you can get the sound from the TV's internal tuner into the receiver.
3) If you have a basic AV receiver unable to do sound from HDMI, then connect up as you have in your diagram, but with digital or analogue audio connections from the DVD-R, Humax and TV to carry sound. Or you can connect the DVD-R and Humax through the receiver, and then on via an HDMI to the TV, but with additional digital or analogue audio connections to the receiver.