What is the ruling on one who delays attending congregational prayer in the mosque due to fear of crowds, and is it permissible for him to appoint someone to perform Hajj on his behalf given his suffering from claustrophobia and agoraphobia?

Fear of crowds and enclosed spaces is a pathological fear that must be overcome and for which a specialized doctor should be consulted. Steps for treatment include: attending congregational prayers, going early to prayer, and competing for the first row, as obedience to Allah brings security and comfort. Seeking medical treatment is permissible, but authorizing someone to perform Hajj on your behalf while you are capable is not permissible. This illness is not a religiously acceptable excuse for Hajj; rather, it can be treated. As for praying alone behind the row, there is a difference of opinion regarding it. The majority consider it valid with dislike, while the Hanbalis consider it invalid. Sheikh Al-Islam Ibn Taymiyyah considers it valid with an excuse and invalid without one. If your son is next to you and is discerning (mumayyiz), then the row is formed with him, and you would not be praying alone.