Presumably you just record at what time you reach a way point. If horror of horror happens and someone has been hacking / jamming the GPS system, you can do the maths to work out roughly where you are?
No; I don't do anything. I just fly the planned route. See some trip writeups on my website. You would not want to do those using dead reckoning.
There is no need to know the ETA at each waypoint. In practice one flies at a chosen power setting. 23" / 2300rpm / 11.5 USG/hr gives me 138kt IAS (at low altitudes) and that's what I fly at. I will get to where I am going when I get there
At high altitudes, one is limited (non turbo) by the available MP, so e.g. at FL100, best economy, I might be doing 140kt TAS on ~ 9.5 USG/hr, and I can't do any more because the motor is sucking all it can suck, and it would be stupid to fly slower. Same all the way to about FL170/180, above which one needs a higher fuel burn (and max revs).
If some ATC unit asks me for the ETA to somewhere, I read it straight off the GPS
If GPS got jammed, which has happened (off Italy, 2004, for a few minutes) but is exceedingly unlikely, I would fall back to VOR/DME - and fly the same route. If the GPS unit itself packed up, I have 2 others (at least) kicking around; a G496 in the yoke, and usually I run a tablet computer with a VFR moving map on it.
I can hardly believe we are still having this debate in the 21st century. But nothing suprises me in aviation. The JAA IR ground school was approx 95% totally useless garbage. Stuff tossed out by the RAF due to irrelevance back in the 1970s.