10 days - Germany, Prague, Austria, Italy

Day-1 Reach Munich at 4:10 PM. Munich Airport to Prague by leoexpress bus.

Please note that you will catch the Leo bus (18:15) only if your flight is on time. And the current timetables don't show a later bus to Prague (shortly after midnight there is a Flix bus - but do you want to spend the night in a bus?). You might consider to spend the evening in Regensburg (beautiful historic old town) and continue the next morning by bus or train (buses on www.busliniensuche.de, trains on www.bahn.com).

reach Munich and night stay near Airport, probably Freising ?

Yes, or Erding, which has a great spa.

Day-9 [...] stay at Brenner or Innsbruck.

Brenner is not a lovely place to stay. I'd prefer either Sterzing / Vipiteno in South Tyrol or Matrei am Brenner in North Tyrol or somewhere in the outskirts of Innsbruck where you can park your car (parking in or near the center is expensive). A beautifully located but simple hotel would be Gasthof Ölberg (Höhenstrasse, halfways between the center and the Seegrubebahn cable railway). From the terrace, there is a spectacular view of the city and the southern mountains.

so it would look rush.

It will be rush.

Day-1 Reach Munich at 4:10 PM. Munich Airport to Prague by leoexpress bus.

At 7:20pm there is a flight from Munich to Prague, which might be more comfortable (about $200).

while you might not like hearing this, I would remove the Prague part of your trip.
we have driven and visited much of your proposed trip and I could not think of doing it in 10days. IMO it would be a waste. you will spend most of your time driving and miss so much. particularly if you like photography etc.
Leave Prague for another trip and spend more time covering a smaller area.
If you have a car near Salzburg then design a route that allows you to not back track. stay in some of the beautiful Pensions that are in the general Ramsau area, rather than staying in Salzburg hotels etc.
similarly there is so much to see in and around the Dolimites, rather than 'just driving' through.

hope this helps.

Thank you.

Probably we can skip Prague. In this case, I can pick car from Munich and drive to/around Salzburg. Would you like to suggest some recommendations ?
It is fine with us, to not stay in Salzburg and make base in other nearby areas.

If I am skipping Prague and reaching same night (Day-1) to Salzburg area, still it would be difficult to give time to Dolomites later ?

Why would you want to drive to Salzburg instead of taking the train? After a long flight the train is much more relaxing and safer. The motorway between Munich and Salzburg is almost always crowded and stressful, and parking in Salzburg is expensive. Take the S8 from the airport to Munich East ("München Ostbahnhof" - no need to go all the way to the main station) and transfer to the Meridian train to Salzburg; there is a connection every hour. A Bayern ticket for two is €31 (please note: it does not include local transport within Salzburg). Pick up your car in Freilassing when you are leaving Salzburg to avoid the drop off fee..

Day-6 Leave Salzburg in rental car [...] night at Lienz

It's much nicer (and also cheaper) to stay on the southern ramp of the Großglockner road, either in Heiligenblut or in one of the small villages south of it, say Großkirchheim or Döllach.

Alright, I will be skipping Prague and will be taking train from Munich to Salzburg on first day. Including first night, I will will have 4 nights, before I leave towards Bruck, Lienz, Cortina.
I would keep one day for Salzburg and may be rest 2 days for surrounding areas with driving. I read few posts suggesting to stay in other areas rather than Salzburg. Can you suggest, which place would be appropriate for doing day trips to Salzburg and other loops rather than repeating same roads ?

Also, would it be better to keep 4th night towards my route of last day, like near Berchtesgaden or further ?

one option to investigate is staying or visiting the Bechtesgaden or Ramsau area. ( south of Salzburg)
https://www.berchtesgaden.de/en/home
the quaint towns have all the painted buildings that you would expect and the accommodation is very reasonably priced and a great experience.
there are so many options to fill a few days in the general area. some potentially full of tourists, others not so much
with a car you could easily drive around to these.
eagles nest, document centre, salt mine, hikes into the mountains, the list goes on.
last year ( and on another trip) we elected to stay in beautiful Pensions(rather than hotels) there and drive into salzburg ( there is a park and ride system- on the outskirts of salzburg) for the day.
if you want to visit salzburg but not stay in the city.

One night we went to the therme in Beschtesgaden ( for something completely different)
https://www.watzmann-therme.de/
also look at
https://www.salzburg-burgen.at/en/hohenwerfen-castle/
https://www.rossfeldpanoramastrasse.de/en/panorama-street/description/
https://www.uncommon-travel-germany.com/konigssee.html

do a search in the tab at the top of the page, for previous posts.
hope this helps.

I spend more time in reading and it looks like, we can have two options -

1st night - Pick car from Freilassing, drive to Wolfgangsee, spend evening there and stay nearby.

2nd day - Leave hotel, visit Hallstat, leave to stay overnight at Berchtesgaden

3rd day - Day trip to Hallstat, overnight at Berchtesgaden

4th day - Day spend nearby. (yet to decide, what should I fill in this day), overnight at Berchtesgaden

5th day - Leave towards Bruck, Grosssglockner road.

Another option is, keep only one base Bechtesgaden and do day trips from there. Which makes more sense ?

Also, though there are lot many places, any recommendation for 4th day ? Berchtesgaden national park ?

2nd day - Leave hotel, visit Hallstat, leave to stay overnight at Berchtesgaden

3rd day - Day trip to Hallstat, overnight at Berchtesgaden

Why would you drive nearly two hours from Hallstatt to Berchtesgaden just to sleep there, and return the next mornig to Hallstatt by again two hours driving?

Sorry, I made a type. Please read this day as -

3rd day - Day trip to Salzburg, overnight at Berchtesgaden