Man writing romantic letters to his former wife

Firstly: 

After a woman has been divorced and her ‘iddah is finished, she becomes a “stranger” (i.e., non-mahram) to her former husband, so it is not permissible for him to correspond with her or talk to her or shake hands with her or be alone with her. Such actions on his part or on hers pave the way for immorality, let alone being haraam in and of themselves. 

1 – Shaykh Muhammad Saalih ibn ‘Uthaymeen said: 

It is not permissible for any person to correspond with a woman who is not his mahram, because of the fitnah (temptation) involved in that.  The person who is sending these letters may think that there is no fitnah involved, but the Shaytaan will keep at him until he tempts the man by means of the woman and vice versa. 

The Prophet (peace and blessings of Allaah be upon him) commanded those who hear the Dajjaal to keep away from him, and he said that a man may come to him as a believer, but the Dajjaal will keep at him until he tempts him and leads him astray. 

There is a great deal of temptation and danger in correspondence between young men and young women, so they must keep away from it, even  though the questioner may say that there is no love involved. 

Fataawa al-Mar’ah al-Muslimah, 2/578 

2 – Shaykh ‘Abd-Allaah al-Jibreen said, when he was asked about corresponding with a non-mahram woman: 

This action is not permissible, because it will provoke desire between them and will make them want to meet one another. This kind of correspondence often causes fitnah (temptation) and plants the seeds of zina in the heart, which leads to evil actions. So we advise those who are seeking that which is in their own best interests and who wish to protect themselves to avoid writing to or speaking with non-mahrams, etc., so as to protect their religious commitment and their honour, and Allaah is the Source of help. 

Fataawa al-Mar’ah al-Muslimah, 2/578, 579 

Secondly: 

It is not permissible for a husband or a wife to keep pictures of one another after the ‘iddah following talaaq has ended, because they have become strangers (i.e. non-mahrams) to one another and Allaah has forbidden them to look at one another. Allaah says (interpretation of the meaning): 

“Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts). That is purer for them. Verily, Allaah is All‑Aware of what they do.

And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts)”

[al-Noor 24:30-31]

Moreover, for the husband to keep pictures of his former wife in the bedroom of his new wife is contrary to good treatment of the new wife, and it will generate jealousy and hatred towards the first wife, and rancour and hatred towards her husband. 

Hence it is not permissible for the husband to keep pictures of his former wife or to correspond with her. 

If the divorce is not the third and final talaaq, in which the husband is not permitted to take back his wife until after she has been married to another husband, and if the husband thinks that the reasons for the divorce no longer apply and that they can adhere to the limits set by Allaah and that each of them will be able to treat the other properly, then in such a case he can take her back with a new marriage contract so that she will be his wife again, especially if he has children from her whom he fears may be adversely affected by their parents’ separation. 

Marriage to another woman does not mean that he cannot re-marry the divorced wife if he thinks that he is able to take care of both.

 And Allaah knows best.