I travelled for two years in Europe before meeting DH and I always bought train tickets on the day or a few days before. I never had a Eurail pass or anything, I just bought point to point tickets and it was great. Visa-wise, it's exactly as Ksand said. Since my trip was longer than usual, I balanced my Schengen zone time with time out of the zone so I was never in the zone more than 90 days in a 180 day period.
Unless their honeymoon will be longer than 90 days, they should be fine.
It's a different story if they plan on going to Turkey:
http://www.independent.co.uk/travel/news-and-advice/turkey-us-visa-services-suspension-citizens-travel-ban-embassy-row-latest-a7996541.htmlRegarding trains, each country has their own rail company (Deutsche Bahn in Germany, SNCF in France) so it's best to look directly on their website to see what routes are possible and what prices are like.
If they really want to buy tickets beforehand, there are companies that will do it, but I think it's usually not necessary. My parents used Loco2 (I think) and while they did save on one journey, we could have just as easily bought them at the station on the day since most trains were regional trains and the prices didn't increase.
Where are they going? Long journeys might be better to book ahead, but can sometimes be done on that country's rail website so there's be no need to go through another company.
Here's a short FAQ on train travel in Europe:
https://www.ricksteves.com/travel-help/rail-faqFrom that page:
Do I need a rail pass in the first place?
As a rule of thumb, a pass is worth considering if you're traveling by train on at least three separate days. It all comes down to whether the pass would save you money over simply buying point-to-point tickets.