as time goes by, and by. So in the future years (weeks/months/etc).

Definitely 'expand'.

Produce is actually a really good word, and you run the risk of sounding pompous if you over think it, but how about supply? They confirmed they couldn't meet demand. They confirmed production couldn't meet demand. They confirmed they could not supply enough to meet consumer demand.

There are many aspects to this. Yaw is a term used in flying (along with pitch, and roll). Yaw ten degrees in a plane would be to raise the nose up 10 degrees. We are go for touchdown means we are ready for landing, the wheels or landing gear is in place and everything is as it should be. Strictly speaking the grammar is wrong. However it is used partly as a shorter version for speed, but also partly to keep instructions clear because over long distances radios and other devices have not always transmitted quality sound. Simple words such as 'go' are less likely to be misheard or misinterpreted.

Yes, in Britain we have 'flight(s) of stairs, and set(s) of step(s). Steps would take you up to a split level, or a front door etc. If you go to a full floor or more it is a staircase or stairway or a flight of stairs. This is relaxing here, and you do occasionally hear set of stairs, but this is less common.

I anticipate having an enjoyable working relationship with you all. I expect (to have) an enjoyable working relationship with you all. I look forward to having an enjoyable working relationship with you all. I reality most people would use these interchangeably, but 'anticipate' is more formal, and the meaning is slightly different. It implies more that you expect it, or regard it as a forgone conclusion. Look forward to is more natural to the native ear.

Because in this sentence the focus is on the singular 'time difference' not the number of hours.

'Clarify' is farily common in Britain, it would not stand out as unusual.