Schmalle

The logical conclusion of what is described in the OP's second paragraph is that the low level has nothing to do with the HX Stomp. It's at the mixer side.

The Dual IR block has a Delay parameter which you can use to phase align IRs. Set it neutral / to zero.

Cioks DC7 provides 6 W per outlet. You needs at the very least 10 W to operate. So you need a current doubler adapter cable and connect HX FX to two outlets.

In Command Center you can set up footswitches per preset. The CC Toggle Commands you're using offer Latch and Momentary as switching options.

Like @enjaltsuggested Command Center's Preset Command does what you want on the Stomp itself. So if you program a footswitch to reselect itselft you can then externally trigger that footswitch with MIDI CC#48+X where X is the footswitch number. A bit clunky but it works.

That behavior is selectable in the switching type option: latching vs. momentary.

There is no preset reload option for incoming PC messages. But there is a Reload option for snapshots in Global Settings -> Preferences -> Snapshot Reselect. With that you can send a MIDI CC#69 (Snapshot Select message) to restore a preset if you know what snapshot it is selected initially. This also works when you program your MIDI foot controller to send a combination of MIDI PC *preset number* followed by MIDI CC#69 *snapshot number*.

The Powerplant has a hint written on the side: "Max combined current for all 9V DC outputs: 500 mA". The HX Stomp consumes about 900 mA when running. So the Powerplant doesn't provide enough current / power for the Stomp.

Search for E Bow or Sustainiac - these are common solutions for getting infinite feedback without volume. That said you can generate an artificial feedback sound with predefinded pitch without even using the guitar. I attached a sloppy HX Stomp preset to give you a starting point. You don't even need the Feedbacker. Just use one or two 3 Note Oscillators feeding the amp. Make it footswitchable (Bypass Assign). Let it fade in with the Attack parameter. Add something like a Pitch Vibrato to let it become more alive. Go crazy and change the oscillator pitches via Contoller Assign or Snapshots. Be creative! FB Generator.hlx

Use the Four Cable Method [the manual explains it]. Add the Boss between the HX Out and the amps return jack.

"-28" is a boot failure and the comments suggest it's hardware related. Sometimes rebooting helps. Sometimes it's unresolvable without a hardware service. Open a support ticket.

MIDI is used to change stuff on outboard gear by sending messages. Those messages can be of several types. Most used are PC (Program Change) messages to trigger program (preset) changes and CC (Continous Control) to control parameters on other devices. Your picture shows a CC Toggle set up but for changing presets you need a PC command.

That cable should be fine. Cable from Helix MIDI Out to Boss MIDI In. Global Settings > MIDI/Tempo > MIDI Base Channel = OMNI (or the channel that the Boss is set to) Global Settings > MIDI/Tempo > MIDI PC Tx = ON Now changing presets on the Helix should trigger the same preset number on the Boss. Once that works you can set Global Settings > MIDI/Tempo > MIDI PC Tx to OFF and program each patch or snapshot or footswitch to perform a MIDI PC (program change) via Command Center.

Yes. The Paint Audio MIDI Captain DUO is compatible with the HX Stomp (XL) and you can program it to change presets using MIDI PC (program change) messages. Other stuff like controling effects or changing snapshots works, too.

The only way I can think of is using a Send block in front of each amp model. You'll then have to mix the two signals externally. Some amps have multiple inputs.