Q* - this is a known fault at the moment on ba.com. The listed route on MyFlights often is strange, it normally is fine on the mobile app. What does the BA app say regarding ticket numbers on each segment?

Q1 - You should indeed get all BPs at PEK. All BPs can be downloaded to one phone on BA. The IB app will simply ask if you want to download or e-mail the Wallet boarding passes, you can then add them one by one into your Wallet. There are no mobile boarding passes from Beijing.

Q2 - if PEK can't issue your MAD-GRX boarding pass then try getting it by checking in online on the Iberia website or app. It might just say "your first flight is operated by another airline" and won't let you, though. You don't have too long at LHR, but if you want to try getting your MAD-GRX boarding pass there then head to the lounge (perhaps Guest Services is best) or to a flight connections desk, it doesn't matter.

Q3 - just before immigration and flight connections, as soon as you turn off the main walkway spanning the entire terminal. There's an IB desk on the right, connections to gates RSU on the left and immigration straight ahead. You'll need to clear immigration here, take the train, clear security then you'll be in the T4 departures area. Note the lounge in T4 will be closing end of Oct.

Q4 - you should get a wheelchair, it really is quite far, especially if your MAD-GRX is an Air Nostrum job. I wouldn't get it at LHR, they are severely understaffed/messy and I wouldn't risk a 75min connection with assistance. You can book it with either BA or IB, it doesn't matter, but perhaps best to double check with IB anyway. You should ask at the gate at LHR to confirm that you will receive assistance from disembarking in MAD to your next gate.