What is the Zaydi explanation ? Do Zaydis believe Imam Ali (as) had the knowledge which was given to Khizr (as)
Also do Zaydis believe Prophet Idris (as), Prophet Ilyas (as), Prophet Isa (as) and Khizr (as) are still alive ?
As far as I've read, al-Khizr (as) is considered a prophet. In the Lawama al-Anwar of Imam Majiddin al-Muayyidi, rahim Allah, he relates instances where al-Khizr (as) visited some people during the time of the imams and he refers to him as "Nabi al-Khizr" which indicates that he is indeed a prophet. This should also answer your question regarding whether he is alive or not.
Also in our tafsir books, it is said that al-Khizr (as) had knowledge that Musa (as) didn't possess and Musa (as) had knowledge that al-Khizr didn't possess.
Regarding Imam Ali's, alayhi as salam, knowledge, it is simply the knowledge that was taught to him by the Prophet, peace and blessings be upon him and his progeny. It is not a mystical thing as the 12ers make it out to be. So, when he predicted the flood of Basra, it was because this was conveyed to him, alayhi as salaam, and not the result of some type of mystical knowledge.
Regarding the Prophets Isa and Idris, peace be upon them both, I believe that the Zaydi view is similar to that of the rest of the Muslims and that is that they are both alive.
I don't think Ilyas (as) is alive.
Allah knows best!
From what I learned that it is possible for a man to connect with Allah (swt) through 2 ways. One way is through wahi and the other way is through a created medium. From what I've been told is the that wahi is only restricted through Prophets but the other method can be done of communication can be done through a pious person. What is the Zaydi view ? Are all forms of communication with Allah (swt) through Prophets only ?
Do these Prophets that are alive still communicate with Allah (swt) through a created medium ?
Yes. The answer to your question is in the Book of Allah. The Qur'an mentions instances where non-Prophets received divine communication. Interestingly enough, the verb form of wahi is used in these cases. For example, when it says that the mother of Musa (as) was insipired to place him in a basket or when the divine communication reached Maryam with the aid of Jibril, this could be seen as wahi but it is distinct from the mission of the Prophets and Messengers (as) in that the latter are commanded to convey the message and are endowed with infallibility.
Regarding whether the Prophets that are still alive still receive revelation or the like, i dont think so. This is because the Messenger of Allah, peace and blessings be upon him and his progeny, is the seal of the prophets. Those Prophets that are alive have a function that they must fulfill and it does not entail that they convey any divine revelation. This is far as i know and not an "official Zaydi" position.
Allah knows best!
عن شهر بن حوشب، قال: بلغني أن رسول الله صلى الله عليه وآله وسلم قال: في المحرم ينادي منادى من السماء: ألا! إن صفوة الله من خلفه فلان، فاسمعموا له وأطيعوا، في سنة الصوت والمعمعة.
“Shahr ibn Hawshab (RA) narrates that the Messenger of Allāh (sawas) said: In (the month of) Muharram, an announcer will call out from the heaven: beware! Surely, (be informed that) such a person has been chosen by Allāh, so listen to him and obey him during the year of uproar and turmoil.” Ibn Hammād related it in al-Fitan (1:226,338#630,980); and Suyūtī copied it in al-Hāwī lil-fatāwā (2:76).
Also look at this narration.
عن علي رضي الله عنه، قال: قال رسول الله صلى الله عليه وآله وسلم: المهدي منا أهل البيت يصلحه الله في ليلة.
Alī (RA) relates that the Messenger of Allāh (sawas) said: Mahdī will be from my family. Allāh will turn him overnight into a righteous person
Ibn Mājah related this Hassan (fair) hadīth in as-Sunan, b. of fitan (turmoils) 4:454 (#4085); Ahmad bin Hambal, al-Musnad (1:84); Bazzār, al-Musnad (2:243 # 644); Abū Ya‘lā, al-Musnad (1:359 # 465); Ibn Abī Shaybah, al-Musannaf (7:513 # 37644); Daylamī, al-Firdaws (4:222# 6669); and Suyūtī in ad-Durr-ul-manthūr fit-tafsīr bil-ma’thūr (6:58).
Also please make sure of the issue of Allah's communication with humans. I think prophet-hood is the only medium.