Assalamualaikum ustaz. What is meant by khitbah or fiancé?
Waalaikumussalam wrt. wbt.,
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions, and all those who follow his footsteps until the Final day.
Fiancé according to the 4th Edition of Kamus Dewan  is defined as:
- Future wife or husband
- Promise or agreement to be husband and wife (marry)
- Asking a woman to be one’s wife
- Ask in marriage
Fiancé or in Arabic Khitbah (خِطْبَةِ) is stated in the Quran by Allah SWT. Allah SWT states:
وَلَا جُنَاحَ عَلَيْكُمْ فِيمَا عَرَّضْتُم بِهِۦ مِنْ خِطْبَةِ ٱلنِّسَآءِ
“There is no blame upon you for that to which you [indirectly] allude concerning a proposal to women,” 
Although this verse explains the permissibility of proposing to a woman who is in her iddah, however, the generality of this verse signals the permissibility of proposing to a woman one intends to marry.
Al-Khatib al-Syarbini defined khitbah or a proposal as a request for marriage from a man to a woman. 
Sheikh Dr Wahbah al-Zuhaili stated that what is meant by الخِطبة is a proposal from a man where he is asking to marry the woman through a clearly understood method. 
According to the above question, simply put, getting engaged is the act of proposing and stating the intention of getting married to a woman. This is based on the act of the Prophet PBUH who proposed to Aisyah R.Anha and also proposed to Hafsah R.Anha.
However, it should be reminded, that there are several types of women that one cannot propose to, they are:
- A woman who is in iddah raj’iyyah even if it is just an allusion (ta’rid)
- An engaged woman. This is in accordance with the hadith of the Prophet PBUH by Ibnu Umar. He said:
نَهَى النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ أَنْ يَبِيعَ بَعْضُكُمْ عَلَى بَيْعِ بَعْضٍ وَلَا يَخْطُبَ الرَّجُلُ عَلَى خِطْبَةِ أَخِيهِ حَتَّى يَتْرُكَ الْخَاطِبُ قَبْلَهُ أَوْ يَأْذَنَ لَهُ الْخَاطِبُ
“The Prophet (ﷺ) decreed that one should not try to cancel a bargain already agreed upon between some other persons (by offering a bigger price). And a man should not ask for the hand of a girl who is already engaged to his Muslim brother, unless the first suitor gives her up, or allows him to ask for her hand.” 
Al-Khatib al-Syaribini said the prohibition is issued because such an act may hurt others. 
As for the usual custom of exchanging rings, and gifts and visiting the woman’s house is a permissible custom and it doesn’t contradict Islam. It is a symbol of the sincerity of wanting to make the woman his wife. As long as the custom doesn’t contradict syarak, then it is permissible. The matter should also be agreed upon by both parties and should be followed with determination and resolve. From Abu Hurairah RA, the Prophet PBUH said:
وَالْمُسْلِمُونَ عَلَى شُرُوطِهِمْ إِلَّا شَرْطًا حَرَّمَ حَلَالًا أَوْ أَحَلَّ حَرَامًا
“Muslims must keep to the conditions they have made, except for a condition which makes unlawful something which is lawful, or makes lawful something which is unlawful.” 
However, the matter that should be understood and considered properly is that getting engaged is not a license to interact freely. Acts such as going out together just the two of them to shopping malls, eating and others are completely prohibited. The reason is an engaged man and woman are still considered strangers. Even more so it is prohibited to only be together alone in a quiet and secluded place. This is based on the statement of the Prophet PBUH:
وَلاَ يَخْلُوَنَّ رَجُلٌ بِامْرَأَةٍ, فَإِنَّ ثَالِثَهُمَا الشَّيْطَانُ
“Whenever a man is alone with a woman the devil makes a third.”
May Allah SWT grant us all a clear understanding in this religion.
 Surah al-Baqarah: 235
 See Mughni al-Muhtaj, 3/135
 See al-Tafsir al-Munir, 2/376
 Narrated by al-Bukhari (5142)
 See Mughni al-Muhtaj, 4/159
 Narrated by al-Bukhari through muallaq before the hadith (2274), Abu Dawud (3594), al-Daruqutni (3/27), and al-Hakim (2309).