Does a stream winner who practices vipassana tend to have a feeling being oblivious to most of things he thought was very important before.It's a feeling as if things don't really be marked in the mind as very important as it used to be. Is it possible to happen?
It's possible but not necessarily a sign of having entered the stream. If someone engages is vipassana meditation for a couple of decades f.i. there can also be an increased lack of interest in things or forgetfulness. Just due to increased habituation of new ways and natural wear-and-tear of old habits which are no longer supported.
To be on the safe side: I would suggest to see it as a sign progress and of effective meditation rather than as a sign of being a stream-enterer.
Making self first = taṇhā, māna.
The reasonable truth for enlighten nibbāna, 4 sacca, is very important before for ariya. So, 4 sacca is called 4 ariya's sacca (4 noble truth of ariya; catu-ariyasacca).
If that ariya's conversation partner talking inside 4 ariya's sacca, that ariya must make his partner's word important before his word, because of suppurisa sutta.
But if ariya's conversation partner talking out of 4 ariya's sacca. He maybe stop to talk with, or he will make his thought important before, if he think that he can teach his partner to enlighten.
It's a possible sign of progress, yes. If such would not arise, there would not have been much progress. How ever, it can be that such is based on eternally intelectuall reasoning, which could be possible even based on wrong view. Such might be even more worse than no progress or effect by vipassana.
It's good to assosiate much with people of right view, not tending to what ever extreme but see and teach cause and effect in proper ways.
It's usuall that those would tend to cross-question you often and of course people just knower of the Pitakas and even those who have mastered Jhanas might be not sufficent enought to be supporter. If there have been progress, one would not have that much difficult to figure out of whom might be a helpfull noble one.
Another sign of having made unchangeable progress is that one has no more doubt and has grown "independent" in regard of the Dhamma and way of practice. Of course useful merely literary knowledge he/she might still be able to nurish well in addition, but mosty just as good livelihood/ good entertaining of the mind.
A useful guide for further undertakings is this collection of Suttas: Into the Stream - A Study Guide on the First Stage of Awakening
Much success and mudita!
Sole dominion over the earth, going to heaven, lordship over all worlds: the fruit of stream-entry excels them.
— Dhp 178
[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]
Yes, I believe it's a sign of some progress. What kind of progress this is is a whole different story.
By important things you probably mean attachments to things that would typically seem important within an untrained, anxious mind, but due to proper understanding of impermanence and wisdom coming from the teaching - their importance and dependence in contributing to your well-being wanes away.