Salzburg - Transportation from Munich and to Old Town Center

Should be seats available. If not, stand or sit on floor until there are.

Buy tickets at station, no need to buy ahead of time.

Credit cards should be good, but to get cash, don’t get Euro n advance. Get from a bank ATM when you arrive

I understand we would take a train or bus from the Munich airport to the Munich OST to get a train to Salzburg

Corrrect, you take the S8 to Munich East

1.) plenty of open seats on train from Munich to Salzburg? Do I need to worry about no available seats?

I'd go to the head of the train (i.e., in eastward direction on the platform), since most people boarding the train in Munich Hbf (where it originates) are simply too lazy to walk to the front cars

2.) Presume the Bayern Ticket is what we want to buy> (2 adults and 4 kids)?

Yes. The conditions for the BT according to the DB web site:

• Children aged 6-14: up to 3 of your own or other children can be taken along free of charge, regardless of whether the ticket is purchased for one or more people.
• Children under 6 years of age always travel free of charge. They do not need a ticket and are not counted when determining the number of people.

So, it ultimately depends on the age of your children.

And we can just buy this ticket at the Train Station, no need to buy ahead of time.

Correct. Or book it via the DB app, so you don't need to queue up

4.) Can I credit card all the above or should I bring with/immediately look to get some Euro?

Yes for 1) and 2) (no idea re the taxi in Salzburg), but as stated above, it's easier to use the DB app. If you really want a paper ticket then buy from a ticket vending machine in the Munich Airport Center (you can set it to English). Lines at the ticket window can be long.

but to get cash, don’t get Euro n advance. Get from a bank ATM when you arrive

... and avoid that of the Reisebank, which as the worst exchange rate, and look for the local VR Bank Erding or the Sparkasse instead (both have several ATM's in the terminals).

ad 1.)
There is no seat reservation on local trains (i.e. using the Bayern ticket). On express trains I would recommend seat reservations.
ad 2.)
Read the fine print about the Bayern ticket carefully. It is for 5 people at maximum, children under 6 years don't count. Up to 3 children between 6 and 14 ride for free. Express trains may not be used, as well as certain train operators.
There are special fares for groups of 5+, but this depends on the ages of the travelers, and it is not easy to calculate as there are special fares for certain age cohorts, too. If there is a ticket counter at Munich airport I would inquire there.
I think it is better to change trains at Munich Hbf than at Munich Ost.
ad 3.)
Just take two of the waiting cabs in front of the train station. Cab fares are the same for all operators. Tell the driver upfront that you want to pay with a credit card.

Is your hotel located inside the pedestrian areas of the Old Town in Salzburg? If so, it may be just as easy to take the city bus, located right outside the main door of the train station, since you might have to walk a few blocks thru the pedestrian area to your lodging. Your hotel can tell you which buses to use.
We were there last April, and had trouble with the ticket machines accepting our credit cards without a pin#. Instead we booked train and s- bahn travel using the DB Navigator app, which worked perfectly. If using cash, the ticket machines don't like giving out lots of change, so might reject a 20 Euro note for a 4 Euro fare. Learned this the hard way.
Have a wonderful trip, and
I'm sure you're very excited!

rmwaters21, I was glad to see your post as I have just booked the same trip for the spring. Are you planning on getting food at the train station, or on the train? I'm interested in knowing the options/recommendations people have. I'll be landing at 8:30am.

... had trouble with the ticket machines accepting our credit cards without a pin#

In Europe all credit card payments require entering a PIN for amounts beyond a certain value. This value varies between countries and card issuer, but is usually in the range of €25 to €40.

There are special fares for groups of 5+

A DB group ticket for such a small group doesn't have much discount; there is a reason that even whole school classes travel with the Bayern Ticket.

I think it is better to change trains at Munich Hbf than at Munich Ost.

But that would add half an hour of travel time. Even the RJX connection via the main station is a few minutes slower because of the detour. And it costs at least €34.90 per "adult" (i.e., over 14 yo; children under 14 travel free when accompanied by an adult). With four "adults" this amounts to about €140, while the Bayern Ticket would cost €50. Besides, there is much less hectic in Munich East than at the main station.