New to TIVO with Questions

First, as the title reads, I am new to TIVO and still trying to figure out all of the models and capabilities. I need the device for my parents for their Xfinity cable and I am their tech support (ugh). I think that the Premiere4 will work for what they need but I want to ask first rather than get into a device and it not meet the need.

I'd like to know...
With the Premiere4 device will they be able to use all of the "regular" Xfinity cable services - HD channels, On Demand (purchases not required), selecting shows from the guide to schedule a DVR recording.

I read that On Demand wasn't supported when the device was first brought out, but I've seen a post on this forum talking about how people are using the Premiere4 for On Demand -- so maybe support for it has been added.

They have two TVs and I read that the Premiere4 supports the TIVO Mini that they could use for the second TV.

Does the Premiere4/Mini support viewing DVR on the TV attached to the Mini?

Also, is there a monthly charge for the Mini when used with a Premiere4 with Lifetime?

Just curious, can there be two DVR shows being watched at the same time (one on the Premiere4 and the other on the remote Mini)? This is not a requirement, I just want to know in case I get the question.

Thanks for your help!