Since I do much of my work by video link, I have some experience with the problems of conducting business over video-conference.
For permission, in universities it will generally be fine as long as you aren't disrupting the work of others. If there is any rule regulating video, you should be aware of it (e.g., some non-university research institutions don't allow video-conference at all, and make very certain their researchers know).
For quality, I would guess that their actual requirement is not HD, but that they want to be able to read your expression as you talk. Here, the primary limitation is not your camera, but your network connection. The built-in camera for your computer or any cheap webcam will generally produce much higher quality video than you can transmit effectively. Things to do to ensure a good connection:
Use a wired link (e.g., EtherNet) rather than wireless if possible, as your connection is likely to be better and more stable.
Use headphones and a microphone (cheap earbuds with a built-in mike will do): the headphones will prevent echo from your speakers, and the microphone ensures consistent pickup of your voice.
Different software provides different quality tradeoffs optimal for different connections:
- Professional videoconferencing hardware (e.g., PolyCom), is nice if your institution has a room and you can get help using it. Its learning curve is a pain, and it's not any better quality than...
- High-end videoconferencing software (I've had good experience with BlueJeans), provides a fantastic quality connection but has brutal demands for bandwidth and processor power. If I use it for more than ~2 hours on my laptop, it overheats. Note that you don't have to buy this software: generally, only the meeting organizer needs to, and you can connect via a web link that they send you.
- Skype is good for mid-grade connections: it provides nice video when given a consistently good link, but degrades badly if the link is inconsistent.
- Google Hangouts is good for low-grace connections: its video quality is never particularly good, but it will get something through.
The most important thing is the high-bandwidth link: with a good enough link, Skype is generally sufficient within a continent. For very long distance connections (where the limitation is lag and undersea cables) you may want to use higher grade software. If you can't get access to a place that gives a strong connection, arrange the connection for a time when you are likely to have little competition with others for bandwidth. Early morning is generally best: during the day work activities consume bandwidth, and in the evening people are watching video.