Getting from Zagreb to Vienna to Cesky Krumlov to Prague?

I can only address some of your questions.
1. We took the train from Zagreb to Vienna. We stopped for two days en route in Ljubljana, which is totally beautiful. Train from Zagreb to Ljubljana took two hours and twenty minutes. From Ljubljana to Vienna took us 6 hours (2 hours to Maribor, where we changed trains and the hopped on a 4 hour train to Vienna).
2. From Vienna to Cesky Krumlov, we used a great car service. They picked us up at our apartment in Vienna and took us to our apartment in CK. We used this company: www.ckshuttle.cz. It was 80 Euro for the two of us.
3. We used this same company for CK to Prague. It was 80 Euro for two of us also.
4. You will not notice the border crossings on the trains - there's nothing you need to do for these particular countries. Luggage is safe on train if you're alert. I travel light and keep my bag with me under or above the seat. The train station in Zagreb is easy to find and the city trams stop right in front of it. Vienna is more confusing. Take a cab from the train station to your hotel. For the other two cities, if you use the ckshuttle, they'll drop you right off - no cab necessary.
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7. Public transport was no problem in any of these cities and I had no language skills in these countries.

8. We did our trip in October. It started pretty hot down in Dubrovnik. By the time we got to Prague in late October, it was cool, some rain, with highs in the low 60s.
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Have fun!

Thanks for the CK shuttle link. Very helpful.

We also used ckshuttle, from CK to Linz. The driver came to the hotel door, insisted that he carry our bags down to the van in the nearby square. He was prompt and courteous, and the late model van was immaculate. There were, perhaps, two other passengers. It was convenient and comfortable. Don't recall the cost but it was definitely good value for the money. We'd never used such a service before; I hope we won't be spoiled from now on.

This past July we also used ckshuttle to get from Prague to
Cesky with a stop in Kutna Hora, then from Cesky to Vienna. we also used student Agency bus and they are clean efficient and very inexpensive. They are a Czech based company and very good. they may ask for your passport crossing from Croatia to Austria but they check it in front of you. if it is a night train, they will ask you if you want them to hold it so as not to wake you at the boarder crossing. We always say no, just wake us. same with the other crossings. when we were in a private car they checked at the boarder, but on the bus and hdryofoil, no one checked. don't worry.
we used ATMs with no problems in all these cities. we were also in Zagreb. just have your PIN number. In Czech Republic ask the hotel what currency they accept ahead of time. We stayed in B&Bs and they want cash usually. euros were accepted at most of the restaurants and shops we visited.
have a great trip from another Barbara in the public school system.

Here's my take on some of your questions.

"Is luggage safe on both bus and train?"

On a bus, there is luggage storage underneath. Sometimes you are given a baggage check ticket, but usually not. So, if you're really worried, you'll want to look at each stop to make sure no one takes your bags.

On a train, smaller bags go overhead, and larger bags go on a rack in the middle or the end of each train car. If you're really worried, you can use a lock to secure your bag to the rack; I just watch it carefully at stops.

Notice I say "if you're really worried" because luggage theft from trains and buses is one of those things: when it happens, everyone goes on line to talk about it, giving the impression that it's common. But it's not common; those who don't have any trouble (the vast majority) don't say or post anything.

"Is it easy to get a taxi from bus and train to hotel?"

In Prague it's recommended that you call for a taxi from a reliable company rather than taking a taxi from a rank, to avoid getting ripped off (Rick's books have details). In Vienna, taxis are reliable. In Cesky Krumlov, it's a pretty easy walk from the bus station to town.

"Is it fairly easy to get money from ATMs in these cities?"

Yes - the procedure is the same as anywhere else. ATM's are everywhere, and you just insert your card, choose English (or the British flag), and proceed as normal. Do have some idea of the exchange rate, so you will know how many euros and krona you want.

"Is it fairly easy to take public transportation or does one need more language facility?"

No language facility is needed to take public transit in Prague or Vienna; the same skills that work in other European cities apply. The big one is to remember to validate tickets at first use, to avoid getting fined if you are checked by an inspector. And the Vienna subway, like Paris, requires you to open the doors manually at stops.

"Do you have any other highlights or advice or what to look out for, what to buy (souvenirs) or where to eat?"

Start by looking at Rick Steves Eastern Europe. Since you're only in each city for a few days, his recommended highlights are a great template for your visit.

Thanks everyone for your replies. With all my questions, I can't believe I forgot to ask if you need to reserve bus or train tickets ahead of time or can you get them the same day?