>> I now planned to start from Frankfurt and reach Interlaken on 23 November and start again from Interlaken on 27th November (found a couple of train options through GoEuro - suggested a train called DB : hope this is a good option).
DB stands for Deutsche Bahn, the German Railway company - it's not a particular train.
You can plan your trip from Frankfurt to Interlaken Ost and back on the Deutsche Bahn website:
If you book in advance, you can get cheaper fares, but there are conditions attached, so read them carefully.
>> Thun lake and Thun castle on another day.
In November, Schloss Thun (Thun Castle) is only open on Sundays from 1 pm–4 pm, so you could go there on 26 November.
There is information about the boat trip on the Thunersee (Lake Thun) on the page below. At the bottom left of the page is a link to the timetable. Make sure to choose the timetable for 6 Nov to 9 Dec.
>> Followed by a trip to Brienz and take the Brienz To thorn Barn to catch some scenic view and get to a lake Brienz on the third day.
Boats will not be operating on the Brienzersee (Lake Brienz), but you can get there by train, and see the lake from the shore. You won't be able to get up to the Brienzer Rothorn in November unfortunately: neither the train from Brienz nor the cable car from Sörenberg will be operating while you are there.
>> would you suggest me to take an air bnb or hotel to stay ?
Only you can decide what's right for you :-)
Before booking, make sure you are aware of where your preferred accommodation is in relation to transport, how frequent that transport is (including weekends if relevant), and what time the first and last services for the day are. Google Maps has railway stations and bus stops marked, and you can use the Swiss Timetable to plan your trips.
You can search for accommodation to suit your preferences here: