There are situation I cannot go to mosque for jamat (congregational prayer), but my wife is at home. Is it possible that I become imam and my wife is my mukim (I not sure this exact term). What is the rule then? Should we stand in separate row? Can other person can join? Can my wife be imam?
Yes, it is permissible that your wife can stand with you and pray, it will be considered a jamat. but she should not stand right beside you, but behind you.
For further details: http://islamqa.info/en/13757
I'd like to add to the correct answer of Hamza Islam the following:
As OP asked about how the prayer is done. There's one IMO important thing which is not explained: Who should perform Iqamah of the prayer?
Generally scholars agree that a woman can do iqamah and adhan/athan loudly, but it would be better to perform it silently for a congregation of women!
But if the wife prays with her husband it is him who will do the iqamah, not the wife! As in that case she shouldn't speak loudly, as it is a mixed congregation. (See also this fatwa in Arabic).
Note that on the other hand salafi scholars say women don't have to call for prayer (and should pray without any of them) so they don't have to perform neither Iqamah nor Adhan.
And of course a woman can pray with her husband a congregation prayer, but the sunnah is that she prays behind him even if hanafi scholars allow it, if the woman is just near (but "at the side behind") him, so that in case of a tall wife and a short husband during sujud her head would be ahead of his head, as the scholars say it is the position of the feet that counts. (See this fatwa in Arabic)
Note that this could be the case in small rooms.
If the wife prays behind her husband anybody can easily join this prayer, men/boys beside the husband, women/girls beside the wife. If necessary and possible either the husband can step forward or the wife backward to make some space.
I also found this fatwa allowing the wife to say "Ameen" loudly -in a jahr prayer- if she prays with her husband (but not if there is any men considered as a foreigner around) or in a women only congregation. Note that loudly for a woman means that only she and those who are next to her should hear her voice!
And Allah knows best!