It is permissible for a fasting person to exchange affectionate and loving words with his wife (with whom he has done the marriage contract), and it is permissible for him to do some affectionate actions such as kissing his wife or hugging her or holding her hand, if he can control his desire. That is because ‘Aa’ishah (may Allaah be pleased with her) said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) used to kiss (his wife) when he was fasting, and touch (his wife) when he was fasting, but he was the most able of you to control his desire.” Narrated by al-Bukhaari, 1792; Muslim, 1854. 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said:  

A man may kiss his wife, joke with her and touch her without having intercourse when he is fasting. All of that is permissible and there is no sin in it, because the Prophet (peace and blessings of Allaah be upon him) used to kiss (his wife) when he was fasting, and touch (his wife) when he was fasting. But if he fears that he may do that which Allaah has forbidden because he is quickly aroused, it is makrooh for him to do that. If he ejaculates, he has to refrain from eating and drinking for the rest of the day and make up that day, but no kafaarah (expiation) is required of him according to the majority of scholars. As for madhiy (prostatic fluid), that does not invalidate the fast according to the more correct of the two scholarly opinions, because the basic principle is that the fast remains valid and is not invalidated, and because it is difficult to guard against it. And Allaah is the Source of strength. 

Fataawa al-Shaykh Ibn Baaz, 4/202 

This applies only to a man and his wife. As for a fiancée, before the marriage contract is done, the fiancé does not have the right to speak words of affection to his fiancée, or to hold her hand, because he is still a “stranger” (non-mahram) to her and is like any other non-mahram man.  No one should take this matter lightly, and it makes no difference if the fiancée is a Muslim or a Christian. 

We are happy to read your question about fasting among the Muslims, because it indicates that you have a love for knowledge and are keen to learn the rulings of this religion. We congratulate you for that and encourage you to learn more. We ask Allaah to guide you to that which Allaah loves and is pleased with, and we ask Him to create harmony between you and your fiancée, and to help you to marry him. 

And Allaah knows best.