Welcome to Flyertalk and welcome to the BA Forum.

Hopefully it won't happen to you again, but if it does have a look at this thread and also consult with this forum, there are usually experts here - some of whom work for BA - who can give very precise information.

https://www.flyertalk.com/forum/brit...need-know.html

And for claiming EC261 and Right to Care:

https://www.flyertalk.com/forum/brit...261-uk261.html

The BA Forum Dashboard is the main route map to the information threads in this forum.

So this was a less than ideal situation, I'm not clear if you had the BA App, but increasingly / rightly / wrongly the App is linked to robotics which reschedule people. It doesn't always work (I had an irrop yesterday where the App didn't help) but mostly it does. But you should be able to reciaim all your costs and get EC261 compensation for the delay, just use this link
BA.com/complaints
On the final screen, when the reference number shows up, press the down arrow next to the word "..... feedback" and PDF save the complaint. Despite what it says on the screen you may not receive an email copy.

For the phone call cost, yes that may raise some eyebrows since it's so disproportionate. I hope BA will pay this, but I can't be certain since it really should not have come to that. The reason for having Skype (or one of several alternative products) on your phone is not because you want or need it, it's really because you don't want or don't need it.