The sunnah for one who is observing i'tikaf (in a mosque) is not to visit a patient, or to attend a funeral, or touch or embrace one's wife, or go out for anything but necessary purposes. There is no i'tikaf without fasting, and there is no i'tikaf except in a congregational mosque.
Umar (may Allah be pleased with him) took a vow in the pre-Islamic days to spend a night or a day in devotion near the Ka'bah (in the sacred mosque). He asked the Prophet (ﷺ) about it. He said: Observe i'tikaf (i.e. spend a night or a day near the Ka'bah) and fast.
The tradition mentioned above (No. 2468) has also been transmitted by Abdullah ibn Budayl through a different chain of narrators in a similar way. This version adds: While he (Umar) was observing i'tikaf (in the sacred mosque), the people uttered (loudly): "Allah is most great." He said: What is this, Abdullah? He said: These are the captives of the Hawazin whom the Messenger of Allah (ﷺ) has set free. He said: This slave-girl too? He sent her along with them.
حَدَّثَنَا مُحَمَّدُ بْنُ عِيسَى، وَقُتَيْبَةُ بْنُ سَعِيدٍ، قَالاَ حَدَّثَنَا يَزِيدُ، عَنْ خَالِدٍ، عَنْ عِكْرِمَةَ، عَنْ عَائِشَةَ، - رضى الله عنها - قَالَتِ اعْتَكَفَتْ مَعَ النَّبِيِّ صلى الله عليه وسلم امْرَأَةٌ مِنْ أَزْوَاجِهِ فَكَانَتْ تَرَى الصُّفْرَةَ وَالْحُمْرَةَ فَرُبَّمَا وَضَعْنَا الطَّسْتَ تَحْتَهَا وَهِيَ تُصَلِّي .
A’ishah(may Allaah be pleased with her) said “One of the wives of the Apostle of Allaah(ﷺ) observed I’tikaf along with him (in the mosque). She would see yellowness and redness. Sometimes we would place a washbasin while she prayed.”