Forget trying to set it up for the other residents as a group. The staff and administration will likely freak out over the privacy implications and HIPAA laws or whatever. Offer to help other families do it on a one-by-one basis as I outline below:
My mother is in a rest home for the past few months and she's lost the ability to do much of anything on a computer.
Still, we manage to video conference with her every day, with almost no problems and no work required on her part.
The cost was negligible and the setup trivial. Here's what we did:
Scrounge an old laptop. For this, my brother donated a late-model thinkpad. It runs some version of Windows, currently. If it gets a virus, I'll wipe it and install Ubuntu, but it's been fine so far.
Install Skype, with an account created for the elderly person. Set it so that only people on their friends list are allowed to call. Set it to auto-answer incoming calls. Add family members to the person's friends list, but do so carefully, as anyone you add will be able to pop on any time they like.
Add TeamViewer, in case you need to log in and restart Skype, add someone, or even start a movie on Netflix or YouTube.
Our setup has worked well in practice for two years, including scenarios like talking to ambulance crews and LifeAlert, before she went into the home and talking with her doctors and other caregivers at the home. She spends time every day visiting with an infant grandson she hasn't yet met, so it's had a huge impact on the quality of her life.
Some people will complain that they don't like Skype, or they want to use FaceTime, but another family member isn't on IOS or whatever, but by now, everyone knows that if they want to call mom, they just use Skype.