Confirmation of trasnit visa in Beijing Capital for 6 and half hrs transit.

Ali, both of your itineraries are definitely eligible for 24 hour visa free transit.

Anyway, I'm a bit afraid of your very short layover in Beijing within your first itinerary. It is only 2 hours 35 minutes and you have to accomplish quite a number of formalities since you will change the carriers. So, you will have to apply for 24 hour free entry permit and clear the immigration, collect your luggage, clear the customs, exit the transit zone, approach to new check-in, clear the security and arrive on time at the gate for your flight to Baku.

It is theoretically possible, but your time is so tight. If you only travel on a single ticket, it would be quite a different thing, but having two separate tickets will make you literally run from one formality to the next one and also hoping that your flight from Tokyo to Beijing is on time. Usually CA168 is on time, so let's hope that you will manage to catch your next flight.

Please, during your next travel, make a longer layover to avoid unnecessary stress.

I appreciate your detailed response.
In continuation of the previous question, I made another inquiry from China visa center in Tokyo about airlines and they informed me that there might be a requirement for transit VISA to just change the airline from China air line to Azerbaijan airline.
The China airlines also told me that arrival is Terminal No. 2 and departure terminal might be different.
In your opinion, do we need Chinese transit visa if airlines are different?
Thank you in advance.

Everything that I have previously written is valid right now. You are definitely eligible for 24 hour visa free transit in Beijing and you don't need any kind of visa. By the way, calling a visa center or an airline customer service is a huge waste of time because they are not informed or simply don't want to take any responsibility. Those who know is an airport staff and in case that some of them has any uncertainty about your eligibility, you will just point them to Timatic, an authoritative source for the subject that we are talking about. When checking Timatic it is essential that the member of the staff inserts Japan as an origin country, Iran or Azerbaijan as a destination country and China as a transit country. Timatic will immediately show that you are eligible if your transit is less than 24 hours in China.

Trust me, you will write here a few sentences after your travel and you will tell me that I was right :)

Thanks for your kind response.
I will post here the results after my wife made the trip on 24th August.

My wife transfered without any transit Visa requirements in Beijing from Tokyo --> Beijing -> Baku albeit the fact that airlines were different.

China airline (Tokyo to Beijing) landed in Terminal 3 and departure from Azerbaijan airline was from Terminal 2 Gate 2.
No Visa is required. But as the airlines are different, in Tokyo she received just the ticket from Tokyo to Beijing.
In Beijing Terminal 3 custom officer asked for other Boarding passes (Beijing to Baku).
Usually airline in Terminal 2 should issue those passes. But temporary boarding passes were issued in Terminal 3 written by hand :)
Using them, she got on shuttle bus, and after 15 minutes, arrived in Terminal 2.

Thanks for your helpful comments.
Save alot of time.

Ali, glad to read that everything went well :)