are these small enough to travel inside the pole like you would use the plastic push fittings?

Yes, these are small enough to fit inside every section of a XERO Pole

Does this connector set fit a 4mm inner 6mm outer hose?

It will fit a hose just a little bit larger than that. We recommend a 5/16", such as the XERO hose. https://windowcleaner.com/xero-hose

Responding to the answer to my last question. I was told these quick connects wear out, that I should not use lubricant. And purchasing another pair is the best option. At $31/pair at the time I purchased them, I would expect them to last more than 3 months before they seize up. What gives?

I hope you find it more manageable for replacement as we are now selling this at a much lower price due to our change in supplier.

Should I be lubricating these with something? They are getting harder and harder to connect the more I use them.

Quick connects wear out. You should not use lubricant. Purchasing another pair is the best option.

The pieces are indeed snapped in place securely and as deep as possible. There is no blockage. It seems that the male fitting does not engage far enough into the female fitting to trigger the "valve" open. (Not sure what else to call it - backflow preventer?) Anyhow, if I stick the end of the hose in the female fitting it triggers the valve open and water will flow thru the female fitting. But then, of course, I cannot attach the male fitting.

Hi John, It would be easier to troubleshoot via email. jordie@windowcleaningresource.com

What's the trick to getting water to flow thru?!?!? Is it a one-way fitting? I tried it both directions and water won't go thru.

Make sure there is no blockage in the fitting and that the pieces are snapped into place.