What is the authenticity of the hadith: "Three things are a sign of a man's incapacity..." narrated by Al-Daylami, and is its meaning sound even if it is weak?

The hadith mentioned in the question is very weak, both in its short and long versions. Al-Hafiz Al-Iraqi and Al-Albani pointed this out. Despite the weakness of the hadith, the meanings it contains are generally sound.

Firstly: The first sentence about asking for a friend's name: Nothing مرفوع (traced back to the Prophet) has been authenticated regarding it, but its meaning is sound, and weak hadiths have been reported with this meaning.

Secondly: The second sentence about refusing hospitality: Its meaning is sound, and this is supported by the Prophet's instruction for one who is observing a voluntary fast to break their fast and eat from their brother's food, in order to foster affection and remove alienation.

Thirdly: The third sentence about foreplay before intercourse: Its meaning is sound. Scholars emphasize the importance of foreplay and kissing before intercourse, and that the husband should not withdraw from his wife until she has satisfied her needs, as mentioned by Ibn Al-Qayyim and Al-Ghazali.

In conclusion: The hadith is weak in its chain of narration, but its meanings and guidance are sound.