Your concern about details of travel, including transfer times at Luzern, shows that you are being very careful and very thorough. That is a really good way to learn how the system works.
<<"My concern is how far from the platform 4 to 12 at lucern station?">>
Arno has given you a thorough and correct answer.
Since you seem to be worried, and you should not be, because the Swiss train system does not build in transfer times that are too short, here is a link to the station map:
plans.trafimage.ch/luz ern#?lang=en&layer=luzern_i nnenplan&x=666047&y=21 1114&r=0.14
As you can see from the map, all of the trains at Luzern are on one level. You can walk from the rail head for track 4 to the rail head for track 12 in 31.5 seconds, unless there are a lot of crowds, in which case it will take 37.6 seconds. Just joking, but they are very close. Add 3 to 5 minutes to wall along the platforms. However, if you are in a hurry, get on the departing train at any car and walk through the cars until you find a car of your chosen class ( 1st Class or 2nd Class) with empty seats, and sit down. Reservation are absolutely not needed on the routes you mention.
If you take the Golden Pass Route on a train specifically from interlaken to Montreux, there are special trains with panoramic cars from Zweisimmen down to Montreux. Those special cars require reseevtions. But, there are "regular" cars in the same trains, and also "regular" trains, and you can see 98% of the scenery from them, just as well.
My purpose in giving these details, is to help you to help yourself, in case the forum is not available to you, or you are in a hurry for an answer. Use the SB website. The website for the SBB rail system is full of useful information.
For help in using the timetable, the explanation here is quite useful:
You do not need reservations between Luzern and Interlaken.
The Swiss system wants to make it easy for you:
<<"1. Do you meant we just show our half fare card at the SBB counter and buy the reduce fare ticket once we touch down at Zurich Airport?">>
If you choosem, you may forget the SBB counter. Just as Arno said.
You may buy a ticket from a machine or ticket counter. Tell the machine by choosing 1/2 fare, or tell the agent "1/2 fare". No one will need to see your card.
The only time you need to show the half- fare card is when the conductor walks through the train to punch tickets. Then you show your ticket and the half fare card, both.