Can I only use one mp4 video format to play in all browsers?
Yes. You only need to provide one mp4 format to play in all web browsers and devices.
In iPhone, iPad, Android, Chrome, Safari, IE 10 and above, the gallery will use HTML5 to play the mp4 video.
In the legacy web browsers, for example, Internet Explorer 8 and 9, the gallery will use Flash to play the mp4 video.
Firefox and Opera support HTML5, but they do not support mp4. For these two browsers, if you have provided a WebM video, it will use HTML5 to play the WebM. Otherwise, it will use Flash to play the mp4 video.
If your mp4 video does not play in the web browser and devices, one possible reason is your video is not HTML5 compatible. You can use freeware HandBrake http://handbrake.fr/ or FFMPEG https://www.ffmpeg.org/ to re-encode the video.
I am using the WordPress Gallery plugin. What I saw the gallery, in the slider the video automatically starts, but on the iPad Air it doesn’t. The slider waits until you manually start the video.
Is there a way to start the video automatically on an iPad Air, or is this not possible?
It's not possible. Video auto play is disabled on iPhone, iPad and Android. It's a limit by the devices.
About the WordPress Photo & Video Gallery, is the gallery responsive? Can the videos be played in 'auto play' or in sequence?
1. Yes, the gallery is responsive. In the Options tab -> Gallery Option, there is an option Responsive - Support responsive web design.
2. In the same tab, there is an option "Auto slide". If this option is on, the gallery will auto play the image slideshow. But it still won't auto play video.
3. In the same tab, there is an option "Automatically play video". When this option is on, it will automatically play video and if the option "Auto slide" is on, it will play in sequence. But "auto play video" is not supported on mobile and tablets, it's a limitation of the devices.