When I've created a Keynote presentation, is it mobile friendly and responsive to multiple devices?

Yes, it is mobile friendly. If you have special fonts on your Mac, it's possible those may get substituted if you open up your presentation on your iPhone and run it there. But if when I show a Keynote presentation on my MacBook, for instance, my university students are seeing it in all its glory - with the full animations, video, correct fonts, everything. Hope that helps you!

A presentation created in a recent version of Keynote will play on iPad and iPhone.

Its always best to check the presentation when transferred to an iOS device in case there is anything incompatible