Maia, I'll try to help question by question...

The way cycle.travel is displayed on my phone is different to the way described. There are no headers or footers, just "where to...?"

Perhaps you just need to use a finger or thumb to 'slide' the footer into view. I use android but this is my opening screen:

However, if I 'slide' up from the bottom ...

Navigating in a route I can see the elevation by doing the same

Problem. I can drag a route on a laptop but not on iPad or phone. The whole map moves.

I don't think that it's possible to drag a route. It is possible to drag a viapoint. However, using fingers on a phone screen can make the task clumsy and inconsistent. It strikes me that it's simply a case of making sure that a viapoint is selected and practising the pressure/movement of the finger. For example, I find it easier to do with my right hand thumb) than my left!

Problem. The audio directions just stop when out and about. Did get good directions for half the route for the first time.

I can't answer that. It could be something to do with the app's functionality, it could be something to do with IOS,  it could be that settings have been changed, or it could be that the battery is running low and some energy saving process has started.

Again, I'm using android but in 'App Settings' and selecting 'Announcements' you should see something like this

How do I delete routing which has just appeared and isn't wanted?

In Android for a new, unsaved route open on the screen I'll hit the green 'pause' button, then the red 'stop' button that replaces it and I'm back at the empty map.

For a route that has been saved, I'll go to 'Routes', either 'My saved Journeys' or the folder name, tap & hold the name of the route until the option to delete presents itself. Select 'delete' and the job's done. 

Thanks for your very helpful reply.  I guess the issue I have with audible directions stopping is down to loss of mobile signal. Would that be any different your saved route can be used offline?

I used a powerpack when the phone battery got low

I guess the issue I have with audible directions stopping is down to loss of mobile signal. Would that be any different your saved route can be used offline?

I'm afraid I'm not familiar enough with the app under those conditions. In any case, downloading the maps and routes is an easy process and I'd imagine would guarantee voice prompts irrespective of data connection.