Munich/Praque/Vienna/Hallstatt/Salzburg/Munich August by train- suggestions

Advance tickets are not required, but they sure would save you a lot of money.

Prague to Vienna, use the website of the National Czech Rail Service and click English at the top right:
https://www.cd.cz/eshop/default.aspx
Tickets will be from 19 Euro booked in advance

Vienna to Hallstatt use the website of the Austrian Rail Service, OEBB:
http://www.oebb.at/en/index.jsp
Tickets will be from 19 Euro booked in advance

Hallstatt to Salzburg, again use the website of OEBB. The Einfach Raus ticket (details on website) could be used for this trip; this ticket can be purchased on the date of travel at no extra cost. 35 Euro total for group.

Salzburg to Munich - buy a Bayern ticket. Here is a link with helpful details:
http://www.toytowngermany.com/wiki/Bayern_ticket
Price depends on your group size, so can be very affordable.

Regarding the car rental, you wouldn't pass through Salzburg on your way to Hallstatt, so that doesn't make sense. Maybe skip the overnights in Hallstatt and just base yourself in Salzburg, rent a care there and make day trips by car. There are many options for excursions...

Advance train tickets and seat reservations are not required. You can buy discounted tickets 2 - 3 months ahead if you're ready to lock in dates and times, or in the station on the day of travel if you want to keep your plans open. Do you already have hotel reservations that "cement" this plan a bit? Train travel from Vienna to Hallstatt is not via Salzburg; the closest connection point is at Attnang Puchheim, whereas continuing to Salzburg takes you out of your way. I don't see much benefit to a car unless you want to stop at other areas, not listed here, that are not served by train, or unless you have 3 or 4 people to fill up the car.

Hi,

Be advised that going between Salzburg and Munich or vice versa, don't present the Bavarian Ticket on a Railjet train. The RJ train doesn't accept it. That announcement is made in English and German.

I rented a car at the Vienna airport and drove to Piber (by Graz), Hallstatt, and returned the car at the Salzburg airport last month.
It was very fun and roads/traffic weren't bad. I wouldn't drive in Vienna or Salzburg as cars are not neccessary and actually a pain.

Be sure to reserve an automatic if you don't want to drive a manual.

"The RJ train doesn't accept it"

Well, first, RailJet is an Austrian train. Second, no German express trains - ICE, IC, EC - accept the Bayern-Ticket. It's only valid on regional trains in Bavaria, and the RailJet is certainly not a regional train.