From Prague to Cesky Krumlov...

If you want to stop and see other towns, castles etc, then car is useful. If you want to go just to C.K. and Terezin use public transport.
Question#1: It depends where you get better price and conditions. If you can drive stick shift driving is like anywhere else in civilized world. Roads are good. Roads signs are international. If you don't know them, google them and learn them.
Question#2: spend a night in Cesky Krumlov. Driving to C.K. and then Terezin in one day would be too much. You can drive to Terezin or you can return the car and take an organized tour to the camp, whatever suits you better.

a car in Prague is more of a hindrance that anything, parking is limited and expensive plus you will get a car no where near any of the sights.
taking organised trips to both CK and Terezin will probably work out as cheap if not cheaper than renting a car.
Terezin is easy enough to do on your own but it does cover a big area so be prepared to walk a bit.

Krumlov is 200km south of Prague. (It is almost in Austria.) It takes 3.5 hours to get there, so I do not recommend it as day trip. If you want to go to Krumlov, I recommend that you overnight there. Terezin is 65km north of Prague, so in a completely different direction from Krumlov. Therefore I would not try to include both of them on the same trip. Use Prague as a base to get to Terezin, and do it as a day trip. It is easily accessed by public transport.

I hope that this helps.

Thanks, everyone. Marcus, you said it's 3.5 hours one way. Are you taking traffic into consideration, because on the map it is 1.5 hrs away?
We still want to drive, because want to see things around. We wont be driving throughout Prague (I know it might be tough as it was in London).
Thanks.

Terezin - Yes, I would rent a car outside of the city if you want to drive up to Terezin. Don't get a car in central Prague as driving there is quite difficult and can be frustrating with jammed traffic and unexpected construction. A good option might be to find an outlying suburb north of town that is served by the metro or excellent bus system and rent a car from there. With a good GPS it's quite easy to drive to Terezin and parking is also quite simple. We parked at the small fort to visit the prison there as well as the town where people were "housed". Terezin isn't a "camp" in the regular sense...it is a fortified town whose residents were evicted in order to house people temporarily on their way to concentration camps. You'll find a museum there as well as a walking tour of the town with numerous stops at points of historical interest having to do with the holocaust. The town is lived in but still rather empty feeling. To visit both the fort and the town takes most of the day.
If you want to make it easier there is a direct bus from Praha-Holesovice that goes straight to Terezin with just a couple of stops. It costs just a few dollars as opposed to the cost of a rental car and the gas.
If you do take a car then it's worth a stop in the old city of Melnik on your way back. At the top of the hill, overlooking the river, there is a very nice restaurant at the back of the chateau with an outdoor terrace. It has expansive views over the vineyards, rivers, and forests below and is a nice place to decompress after the somber visit to Terezin.
Cesky Krumlov - Technically it's only a couple of hours to drive down to Cesky Krumlov but I would double that estimate. Traffic can be pretty bad. Last time I drove that way, it wasn't bad on the way down but on the way back it took over 5 hours to get to Prague. Completely jammed. Take the train and save yourself the headache. Consider taking the train down in the morning, spending the day and a night in CK, and then taking the train back the next day. It's a bit far for a 1 day trip...you can certainly do it but it's nice to be there overnight when many of the tourists have left. It's a bit crowded during the day.

lina7277, we had a car and experienced driver (recommended in Rick's older books) and it took more like 3.5 hours. It is a long trip.

If you have looked at Google Maps, you must also know that Terezin is in the opposite direction. They should not be combined on the same day just because you have a car. And particularly because camps tend to have public transportation. (I haven't been to that one.)

Rick mentions both the Budjovice Budvar (sp.?) brewery as being on the way to CK, and the nearby "T" towns, which are often classified as of interest for Jewish history. But we didn't have time to see any of that. CK is so far, and has plenty to see in one day. I don't particularly urge you to spend the night, but there is also recreation in the area, like kayaking and forest preserve hiking.

If you have already been to a lot of well-preserved medieval and half-timbered towns, CK is not absolutely essential. But for my special interest, the Baroque theater there was a must-see. In fact, we had been in Prague for the Quadrennial [theater] Performance Design Conference.

Edit: Here's a Rick Steves link for the "T Towns":
https://www.ricksteves.com/watch-read-listen/read/articles/czech-byways

Anita and Tim, thank you for such detailed replies. Maybe I confused everyone (sorry), but it was not our intention to gonto CK and Terezin in 1 day 😊 I was just thinking in rerms of renting a car, since we'll be driving to CK, then might as well drive to T when on our way back to Prague. Based on everything I've read, looks like we will be spending a night in CK.

I am a bit confused about Mala Strana vs. Old Town neighborhoods. Everywhere I read, ppl suggest to stay in Mala Strana. It looks nice, but it seems it is far from the touristy stuff. Am I wrong? Also, if we were to stay in Old town, wouldn't there be a car rental place nearby? Just asking. Will be researching. Thanks.

@Tim: yes spelling of Budvar is correct. Budvar is in Ceske Budejovice. German name for C.B. is Budweis. So original (and better) Budweiser is from Ceske Budejovice, not St. Louis. You can take a tour of Budvar (Budweiser) brewery also in English.
Rick Steves three "T' towns are Trebon, Telc, Trebic. Only Trebic has Jewish history.
@lina: Mala Strana and Old Town (Stare Mesto) are both medieval neighborhoods. M.S. is on the left bank of the Vltava River and O.T. is on the right bank. They are connected by Charles Bridge. It was built in 1348 if I remember correctly. Old Town is flat and Mala Strana quite hilly. On the top of the hill there is the Castle. In both neighborhoods there is plenty to sightsee. Besides they are not that far apart. About thousand feet across the Charles Bridge.
Car rentals are all over Prague. You can google it. You will be always able to find one close to your hotel.

@lina7277, I live in Prague and I have made this journey multiple times, so please believe me when I say that Krumlov is 3.5 hours away from Prague. Also, I really don't see the point of going to the trouble and expense of hiring a car when there is inexpensive, reliable and comfortable public transport available.

As for the difference between Old Town and Mala Strana, there isn't really much between them. Mala Strana is a bit quieter due to the preponderance of embassies in the area - they have something of a deadening effect. Also, the Old Town has a bit more commercial activity, as it is the main body of the city and is closer to more residential neighbourhoods. Unfortunately both neighbourhoods are besieged daily by tens of thousands of tourists.