YES, everything is feasible, but there are so many variables and your travel will be based on the personality of both of you traveling together for 30 days, your budget, railpass, your interests and your “MUST SEE“list. You have listed the main countries and tourist spots but there are so many great places to visit in each of those countries. You need to first, figure out a budget to see how long you can travel. Hostels may run $20.00 – $30.00 per night. So 30 nights x $30.00 is $900.00 on lodging only. many people have posted $75.00 – $100.00 per day excluding transportation so expect $2,250.00 to $3,000.00 You need to do more homework, read all these posts, read guidebooks and decide together on what you want to see and do in each of the main cities and discuss how slow or how rushed you can travel so you don’t kill each other. Since you like nature and hiking, look into Interlaken, Switzerland, stay up at the Mountain Hostel in Gimmelwald, Switz; Cinque Terre, Italy to name a few. Cinque Terre is very crowded in August, so get your plan in order and see if you can get rooms confirmed there asap.
If you have 30 days divided by 2 nights in each city, you can visit 15 cities. But some of these cities, you may want three nights, some 1 night and maybe one or two places for just a day visit if you have more important places that you have to visit. Look up train schedules and make a map listing how far apart each city is by train so you can make a plan. Some cities may be small enough so if you arrive by 5:00pm, you still have 3+ hours to explore, get a good nights sleep, have breakfast and explore in the morning hours and depart for the next city at noon or later and take a cat nap on the train, eat a picnic meal and drink plenty of water so you have energy when you arrive in the next city.