Assalaamu alaykom brothers in Islam, my questions are the following:
1. Considering the fact that the Prophet, sallallaahu ʻalayhi wa sallam, and the four Caliphs did not delegate others to lead the prayer, is it in accordance with the Sunnah to delegate another person to lead our prayer instead of the Amir/Imam of the community?
2. What should a Muslim do if the disbelievers mock the traditional dress of Muslims (like by wearing a thawb at a Halloween party)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.

Saying that the Prophet, sallallaahu ʻalayhi wa sallam, did not delegate others to lead the Muslims in prayer is incorrect. It has been reported that the Prophet, sallallaahu ʻalayhi wa sallam, delegated Abu Bakr to lead the Muslims in prayer during his illness shortly before his death. He, sallallaahu ʻalayhi wa sallam, said, “Ask Abu Bakr to lead the people in prayer.” [Al-Bukhari and Muslim]

An-Nawawi cited the hadeeth in a chapter entitled, “If the Imaam has an excuse, like illness or traveling and so on, then he delegates someone else to lead the people in prayer.”

The hadeeth was also cited by Ibn Khuzaymah in his book Saheeh Ibn Khuzaymah in a chapter entitled, “The Supreme Imaam appointing someone else to lead people in prayer during his illness.”

Anas reported that the Prophet, sallallaahu ʻalayhi wa sallam, delegated Ibn Umm Maktoom to lead the people in prayer, and he was blind. [Ahmad and Abu Daawood]

The rightly-guided Caliphs also delegated others to lead the Muslims in prayer on certain occasions. When ʻUmar was stabbed, he delegated Suhayb ibn Sinaan Ar-Roomi to lead the Muslims in prayer until the Shura Council would choose a new leader to succeed him. There are many similar examples in this regard. It is prescribed for the Muslim ruler (Caliph) to appoint someone else to lead the Muslims in prayer in case of an event preventing him from shouldering this task himself; otherwise, the Muslims may choose the one who has the best knowledge of the Quran to lead them in prayer.

As for your question about what a Muslim should do when the disbelievers mock him, the Muslim is enjoined to adhere to patience, as Allaah commanded His Messenger, sallallaahu ʻalayhi wa sallam, to endure the ignorance and harm of the disbelievers. Allaah, The Exalted, says (what means): {And be patient over what they say and avoid them with gracious avoidance.} [Quran 73:10]

Al-Qurtubi wrote in commentary of the verse, “The verse means, ‘Patiently endure their harms, insults, and mockery and do not grieve at their words or give up calling them to Allaah.’ ‘Avoid them with gracious avoidance' means not to respond with the like of their harms and insults and not to preoccupy yourself with answering to their words because it would constitute giving up the call to Allaah ... Abu Ad-Dardaa' said, 'We smile in the face of some people although our hearts curse them.’” [Tafseer Al-Qurtubi]

Allaah knows best.