Munich, Austria, Prague and Rome

Hi,
The two options are vastly different. What does your heart say:
- Green or white?
- beer or wine?
- Sausage or ham?

More seriously, whatever you choose, you're packing a lot in 2.5 weeks. In that time frame you can do
- Andalucía (6-7 nights) -Barcelona (4 nights) - Rome/Naples (6-7 nights) without Prague
- Prague (3-4 nights) --Austria (6-7)--Rome/Naples (6-7) without Munich
- Munich (3-4 nights) - Salzburg (2) - Vienna (4) - Budapest (3-4) - Prague (3-4) is a new suggestion I have, but it's busy.

You get my drill: you've chosen widely spaced locations so I think you should remove one every time. A flight from, say, Barcelona to Prague will waste the best part of the day including going to/from airport, security, etc.

Thank you, if we choose Munich, Vienna, Salzburg, Prague and Budapest, which is the best way to travel. Is it sort of easy and safe?

If we do Andalucia, travel by plane or train?

Thank you very much for your help.

Munich, Vienna, Salzburg, Prague and Budapest

First point, get the order of these places correct. Look at a map. Salzburg is between Munich and Vienna.
Munich --> Salzburg --> Prague --> Vienna --> Budapest would minimise doubling back. Then fly into the first place (Munich) and out of the last (Budapest).

Is it sort of easy and safe?

Yes, all these places are linked by trains, with departures every 1-2 hours.
I suggest you start reading the Man in Seat 61 website: https://www.seat61.com/Europe-train-travel.htm
He then has sections for each of your trips, for example Munich to Salzburg: https://www.seat61.com/international-trains/trains-from-Munich.htm#Munich-Salzburg
Salzburg to Prague: https://www.seat61.com/trains-and-routes/salzburg-to-prague-by-train.htm
etc. etc.

Rome is an outlier. You should fly there.
If you are arriving 8th October and leaving on 25th October, that is 17 Nights. 5 places at 3-4 nights each sounds good. I don't think you have time for Rome.

Save Rome (and the rest of Italy) for another trip.
And the one after that is Spain (Andalucia and Catalonia).

Salzburg - Prague and Prague - Vienna are indeed more feasible by train than I remembered (respectively six and four hours), so I like that revised order better! Saves the need for a flight or a longer Budapest - Prague train leg.

Regarding Andalucía - Barcelona - Rome: Barcelona to Rome is a flight, Andalucía to Barcelona is a choice. But if you start in Seville, then head to Córdoba and finally Granada (most logical order), best to fly Granada-Barcelona.