One for more information.... I'll continue being a swedish resident with the residence permit of second country

The pass only states what you have posted on the 1st day of travel-I´ve never heard of a possible change in this-so for de dette bli Sverige=SE. I have always used paper passes (nearly 20 by now) so these simply cannot be changed-and I understand the new mobile passes all have to same basic principle.

In fact an old rule stated that one must have lived at least 6 monthes in a country other as ID=only after that time you are beyond allowable stay for tourist and have to register-and hence get some form of document for that. But this is really becoming a grey area and there are no rulings about this to be found-also for the many exchange students etc.
in your case it seems to me best and by far easiest to state SE=Svenska and have to live with the rule of only 2 days of travel allowed in there. You can only use another country if you have official govt document that you are registered there.

So if I can state Sverige as my country of residence and can have multiple trips in another country of residence? Right?

One more question, the pass will not become invalid if I have completed both inbound and outbound trips? If I have still days remaining after completing both inbound and outbound trips

You can't be a resident of 2 countries. You can be a citizen of several countries, but only a resident of one country.At least as far as I know.

As long as you either have a Swedish passport or can prove that you are a Swedish resident you are fine.

You can have multiple Residence Permit according to this:

https://ec.europa.eu/immigration/general-information/already-eu_en#:~:text=second%20EU%20country%3F-,Yes.,permit%20in%20this%20second%20country.

As a long-term resident in one EU country, can I live and work in a second EU country?

Yes. You can stay in a second EU country for more than three months for purposes including work, study or training, if you apply for and are granted a residence permit in this second country.

Ok. But what's important for Interrail is that if you have Sweden as your country of residence on your Interrail pass you must be able to prove your residency in Sweden in some way. If you have a Swedish passport noone will ask questions, if you don't have a Swedish passport you need be able to prove your Swedish residency somehow. 

Sure thanks

I have swedish Residence permit....it will be valid when I will be traveling.

Yes, as Sweden is your country of residence you can travel as much as you like in all other countries, even after you have completed both the inbound and outbound journey.