Elizabeth line from terminal 5 to Hyatt London East

Yes, Whitechapel then 12 minutes walk or a cab.
Almost a 1 hour journey from T5 to Whitechapel.
£13.30 each, pay by mobile methods like google pay etc/contactless or oyster card (if you have one), no group discount

thanks. I am a little confused about the differences in fares amongst the three option - HEX, Elizabeth and regular tube. It seems the station is the same for all three in terminal 5 but platforms are different. When we touch in to enter station and then touch out when we exit White Chapel how does it know which line I took from the airport ?

Also does this amount figure in the daily cap so we can make more travels in Zone 1 after we get to the hotel?

I believe that HEX and Elizabeth line use one rail terminal at T5 and the Piccadilly line uses a separate underground specific station. Each person will need their own payment method. Oyster, contactless or phone. Use the same method tapping in and then out. Phone and the associated credit card can be used separately. So one person uses the phone and another uses the physical contactless CC.

Yes Elizabeth Line is included in the cap, which for Z1 to 6 is £14.10 so basically your next journey costs 80 pence, then all others are free.
If you came HEX the computer would know the route through the ticket gates you use when changing at Paddington, and at Whitechapel the layout of the swipe out exit gates tells the system whether you came by tube or by Elizabeth Line.
Maybe someone who was super clever and knew the station inside out could find side passages around Whitechapel to fool the system, maybe not.o
Technically the tube gets you a few minutes closer to your hotel if you got off at Aldgate East and for less than half the fare, but as you want to use the Elizabeth Line...

There is also a 4th fare from Heathrow to Whitechapel- by taking the Elizabeth Line then the London Overground round the north of London ending at the Overground platforms at Whitechapel. Anyone who took that convoluted route (I can't see any visitor ever doing it) would pay £8.40 for their rail odyssey round London avoiding Zone 1, on that route you have to swipe on the pink routing reader at Stratford to tell the computer your route and be charged the lower fare.

You can't fool the systems. Tube and Elizabeth line have different ticket gates. Elizabeth line departs from a rail station and tube from an underground station.

On saving, if you take Elizabeth line at off peak hours, it is worth considering the zone 1 to 6 travel card with Network railcard. The discounted off peak travel card costs only £10.

Each Network railcard holder can travel with 2 or 3 travel companions. You don't need 3 railcards.

Aldgate East is the nearest station to that hotel but TfL have an annoying habit of not opening the closest entrance if short of staff, so it may not be as near as it should be. Plus you have stairs to negotiate.

could we transfer at Liverpool from Elizabeth line to Hammersmith line to reach Aldgate East which seems closest to hotel?

You can't change at Liverpool, on to the Hammersmith, but you can at Liverpool St for the Hammersmith & City line - full names are really important here.
Whilst you can do the change it's quite a long walk between the two lines there. Personally I would stick with carrying on to Whitechapel and then walking in the fresh air (unless it's raining hard!).

Yes, one stop from Liverpool Street on the Hammersmith and City line towards Barking.

The two stations are actually quite close. You might walk further under ground than you do above ground.

You can get to Whitechapel via the Elizabeth line in 45 minutes - but have to factor in the frequency of the trains, so you can use up some time waiting at Heathrow. Allow up to an hour.

My mother, aged 80, did a version of this route a few weeks ago as she met her sister at that hotel, walking from Whitechapel - and she walked the less than half a mile in seven minutes.

£13.30 due to Heathrow premium, no discounts, part of the zone 1-6 cap of £14.90. Use your device payment method.