If a woman and man both over the age of bar/bas mitzvah converse often via e-mail, instant messaging, and mail is this a violation of yichud? Or does yichud only apply when the two are in person?
Would it make a difference if the woman was the man’s shidduch?
There is no issue of yichud if the two people are not secluded in the same place, and in person. Regarding conversing between a man and a woman, the general rule is that is not permitted because it brings the two people close to each other, which will lead to undesirable thoughts and actions. However what is considered derch eretz, such as saying good morning, and being polite is permitted, or what is needed for a purpose is permitted. Therefore just plain texting, about unimportant things should not be done. this is the general rule regarding the relationship between men and women. there are relationships that require a higher level of derech eretz, such as with family members, etc.
I don’t understand your second question, “if it was the man’s shidduch”. If the two people are dating or engaged and the texting is needed to develop the correct relationship, then it would be permitted. However, if they were dating, and it is no longer for the purpose of marriage etc. then obviously this man or woman is no different than any other person of the opposite gender.
Aruch Hashulchan E:H 21-8,