Can I use the system on my phone & a computer at the same time?

Yes, you can be logged in to multiple devices at the same time.

This could also be a parent or adult Leader and their child or youth member logged in to the same account at the same time!

Remember that if there are two people logged in to the same Scouts | Terrain account at the same time, editing the same thing, then only the most recently saved version of that item will be kept.