Recently came back from a 3 month solo say in EU - self managed.
• You can get an agency to do things for you, but IMO not worth it since the Schengen embassies already delegate everything to an intermedieary (VFS global) and all the instructions and all are laid out pretty clearly already.
• Donno about aged companions. But if you're gonna be in touristy areas no biggie (except things can be expensive). I'm veg too. You can find a few veg options in all tourist-area restaurants. For longer stays, all cities have some 'vegan-only buffet' style places that came in handy.
• Inside country + nearby countries: Train is best. If you don't already know:
https://www.seat61.com/ is THE guide that you need. Book early for better tickets. Book from the right website (eg. Germany -> Czech: Can get better prices on the czech-railway-system-site compared to Germany, for the exact same train). Reservations optional but I go for them for peace of mind. Esp during peak season.
• For within-city travel, I guess if you have aged companions, perhaps Uber - tho it's expensive. Otherwise public transport is excellent in all cities. Same ticket for bus/subway/tram. Go to relevant city's transport website, download app, buy day/multiday/week/month pass.
• Not too much difference between 2nd and 1st class - perhaps depends on train system. I usually got 2nd class but did a 1st class for my last Munich->Berlin journey (since 2nd/1st prices were comparable). That last journey, the train got cancelled and switched to another train. Reservation became, find-any-seat on new train (but still 1st class). Was strangely super crowded - some people had to stand until someone got off. Earlier in my Prague->Vienna trip, I had booked 2nd class with reservation. I guess it was a slow day and my carriage of 30-40 ppl capacity had only 4 people in it.
• The EU Rail pass is only worth it if you're travelling every few days. Otherwise way cheaper to get relevant tickets and be clever about which country's website you buy it from. Again - seat61 is your bible.
• I just got the minimum HDFC ergo travel insurance within a few minutes online on their site.
• Train: seat61 will tell you. Flights: skyscanner.
• PS: If you have connecting flights, remember immigration happens at first point of entry into the Schengen region. I had 1 hour time to catch my connecting flight. I missed it because of immigration (but thankfully was put on next flight by the carrier.