Do we pick partner most similar to opposite-sex parent? Do we pick partner most similar to opposite-sex parent? Do men pick life partner who is similar to their mother? Does it apply to women too? By similar, I mean mostly character/mental features. I dont consider appearance, but It would be interesting to know if that matters.

If yes, is it possible that man (for example) would look for/pick a partner who has character opposite to his mother? What could be scientific reason for that?
Good question. Here is what I found. 

People may be attracted to the physical features that our opposite sex parent posses {1,2} However, the jury is out as to whether people are more likely to be attracted to people who share the mental traits of parents {3,4}. As an example of this {3} write


  "Much of the current research on parental identification and mate
  selection is contradictory and inconclusive. The studies that are
  available suggest a similarity between partner choice and parental
  similarity, although the results for similarity between partner choice
  and parent vary by gender. Various theories suggest that individuals
  choose mates based on some type of similarity with their partners.
  Such similarities include values, religion, physical attractiveness,
  or expressiveness (Bailey et al., 1994; Boyden, Carroll, &amp; Maier,
  1984; Howard et al., 1987; Murstein, 1976). Parental identification
  research also is inconclusive, with some studies finding same-sex
  parent identification and others finding opposite-sex parent or both
  parent identification (Geher, 2000; von der Lippe, 1965)"


I am happy to go into more detail about any of this, if you want me to.

References:

{1} Little, A., et al. (2003). "Investigating an imprinting-like phenomenon in humans: partners and opposite-sex parents have similar hair and eye colour." Evolution and Human Behavior 24(1): 43-51.

{2} Perrett, D. I., et al. (2002). "Facial attractiveness judgements reflect learning of parental age characteristics." Proceedings of the Royal Society B: Biological Sciences 269(1494): 873-880.

{3}van Eeden-Moorefield, B. and E. W. Lindsey (2005). "Intergenerational Effects of Parental Personality and Relationship Traits on Mate Choice Among Gay Male and Lesbian Offspring." Journal of Homosexuality 49(1): 123-143.

{4} Strokoff, Johanna, "Parental influence on romantic attraction with simulated online dating profiles." (2015). Electronic Theses and Dissertations. Paper 2232.
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