Mental challenges of being a telecommuter
Depending on your personality type (whether you are introvert or extrovert mainly), but also external factors like - if you live alone or you have a family - home office situation can take more toll than on some other people.
Apply principles for physical health
Most of the things written in previous post apply also here.
For one, physical health has a huge effect on mental health. Healthier you feel physically, saner you'll feel too.
Another principle is that some recommendations have effect on boths sides. Remember the advice to make strict separation between your work and private life? Lack of separation between work and private life will burn you out quickly. It is an easy trap to fall into, trying to be available for everyone at any time.
Excercise is scientifically proven way to improve mental health. While it's far from the silver bullet for mental health issues (really, it is not), it does help to overall feel better. You just may need to find which excercise (and how much of it) works for you.
Advice not to stuff yourself with snacks and put an effort to eat healthy also applies here. It will not help your long term mental health if you gain weight while working from home. Although, it might give you new hobby for life - trying to get rid of excess weight - which is kind of fun I guess?
Stay in contact with the people (and I mean as close as possible to real face time)
Your company likely has, even if home office situation is new for it, some teleconferencing solution. Even if it doesn't, establish with your own team and teams you work with directly your own standard for video conferencing. Just use same old Facetime or Skype you already use to keep contact with your (grand)parents to stay connected with your colleagues if nothing else is available (if your company doesn't already have preferred video conferencing solution, security concerns around conferencing are apparently not high on its list of priorities anyway).
Slack/Teams/Jabber chat communication is not a replacement for human contact, however much more concise it typically is and generally is supposed to drive productivity.
Also understand that your work mates are different personalities. Some of them might appreciate more frequent check-ins over video calls than others. Respect that.
Keep (or find) off-screen hobbies
No matter how much precaution you put into whole temporary (or permanent, for that matter) home office situation not to make couch-potato out of you, you will likely fail. Increased productivity, easy availability of overtime working hours (due to factors like saving time on commuting, and so on) will in the end be the trap you'll at least partially fall into.
So, find yourself some off-screen hobby. Speaking from the perspective of software engineer - it is easy to make your hobbies pretty much revolve around the things you do - like learning the new programming language or exploring areas of research and development which are outside of your daily scope of duties - but specially when you will be likely spending more time in front of the computer, you should have other hobbies. Some which are more connected to the real world around us.
How does a bit gardening sound, even if it's only about the few pots of flowers in your living room?