Is this a possible itinerary for 30 days?
Not. Remotely. Possible. Even if you halved this itinerary you'd be spending more time and money dealing with transport/location changes than seeing much of anything at all. Then there's the acclimation time to get your bearings in a new location. Just the combo of Milan, Venice, Florence, Rome/Vatican City and Naples would require nearly 2 weeks for just a scratch-the-surface trip.
Traveling with a group adds another layer of complication: you will only move at the rate of your slowest member. That can be an issue when you ALL need to be up, dressed, fed, packed, checked out, and to the station at 7:00 AM, and you need to do that a LOT because of an overloaded itinerary. The more stressed and tired your group becomes due to too many places in too little time, the bigger chance of friction between members.
Who is going to do the research, craft an itinerary to please all 7, order any necessary advance tickets (attractions/rail/bus), choose the accommodations and do the bookings, etc? What's the plan to divvy up costs if rooms or activities, such as day tours, are shared? Do each of you have the same amount of money to work with? Lots to consider here.
Consider as well individual travel experience; have any of you traveled to Europe before? There's a learning curve to everything from efficient packing to figuring out local transport to some local customs, etc. Not everything might work like clockwork, either. One train strike or major flight delay can throw a very tight itinerary into disarray. The one day you allocated for a big hike might be the day it pours rain. Maybe your stomach REALLY doesn't like what you ate last night... 🤢
So, starting deep instead of wide/quality versus quantity leaves you more time and money for sightseeing and fun, provides a more comfortable cushion for figuring out how things work, and some flexibility to manage around what doesn't go according to plan.
...and of course the check points travelers.
Not sure what this means; please explain?