Bukhari :: Book 1 :: Volume 7 :: Hadith 331
Narrated Jabir bin 'Abdullah:
The Prophet said, "I have been given five things which were not given
to any one else before me.
Allah made me victorious by awe, ...
The earth has been made for me (and for my followers) a place for praying and a thing to perform Tayammum...
The booty has been made Halal...
I have been given the right of intercession (on the Day of Resurrection).
Every Prophet used to be sent to his nation only but I have been sent to all mankind.
And then I had to quote this big Hadith, but it is necessary for the answer, otherwise I wouldn't...
Some (cooked) meat was brought to Allah Apostle and the meat of a forearm was presented to him as he used to like it. He ate a morsel of it and said, "I will be the chief of all the people on the Day of Resurrection. Do you know the reason for it? Allah will gather all the human being of early generations as well as late generation on one plain so that the announcer will be able to make them all-hear his voice and the watcher will be able to see all of them. The sun will come so close to the people that they will suffer such distress and trouble as they will not be able to bear or stand. Then the people will say, 'Don't you see to what state you have reached? Won't you look for someone who can intercede for you with your Lord' Some people will say to some others, 'Go to Adam.' So they will go to Adam and say to him. 'You are the father of mankind; Allah created you with His Own Hand, and breathed into you of His Spirit (meaning the spirit which he created for you); and ordered the angels to prostrate before you; so (please) intercede for us with your Lord. Don't you see in what state we are? Don't you see what condition we have reached?' Adam will say, 'Today my Lord has become angry as He has never become before, nor will ever become thereafter. He forbade me (to eat of the fruit of) the tree, but I disobeyed Him . Myself! Myself! Myself! (has more need for intercession). Go to someone else; go to Noah.' So they will go to Noah and say (to him), 'O Noah! You are the first (of Allah's Messengers) to the people of the earth, and Allah has named you a thankful slave; please intercede for us with your Lord. Don't you see in what state we are?' He will say.' Today my Lord has become angry as He has never become nor will ever become thereafter. I had (in the world) the right to make one definitely accepted invocation, and I made it against my nation. Myself! Myself! Myself! Go to someone else; go to Abraham.' They will go to Abraham and say, 'O Abraham! You are Allah's Apostle and His Khalil from among the people of the earth; so please intercede for us with your Lord. Don't you see in what state we are?' He will say to them, 'My Lord has today become angry as He has never become before, nor will ever become thereafter. I had told three lies (Abu Haiyan (the sub-narrator) mentioned them in the Hadith) Myself! Myself! Myself! Go to someone else; go to Moses.' The people will then go to Moses and say, 'O Moses! You art Allah's Apostle and Allah gave you superiority above the others with this message and with His direct Talk to you; (please) intercede for us with your Lord Don't you see in what state we are?' Moses will say, 'My Lord has today become angry as He has never become before, nor will become thereafter, I killed a person whom I had not been ordered to kill. Myself! Myself! Myself! Go to someone else; go to Jesus.' So they will go to Jesus and say, 'O Jesus! You are Allah's Apostle and His Word which He sent to Mary, and a superior soul created by Him, and you talked to the people while still young in the cradle. Please intercede for us with your Lord. Don't you see in what state we are?' Jesus will say. 'My Lord has today become angry as He has never become before nor will ever become thereafter. Jesus will not mention any sin, but will say, 'Myself! Myself! Myself! Go to someone else; go to Muhammad.' So they will come to me and say, 'O Muhammad ! You are Allah's Apostle and the last of the prophets, and Allah forgave your early and late sins. (Please) intercede for us with your Lord. Don't you see in what state we are?" The Prophet added, "Then I will go beneath Allah's Throne and fall in prostration before my Lord. And then Allah will guide me to such praises and glorification to Him as He has never guided anybody else before me. Then it will be said, 'O Muhammad Raise your head. Ask, and it will be granted. Intercede It (your intercession) will be accepted.' So I will raise my head and Say, 'My followers, O my Lord! My followers, O my Lord'. It will be said, 'O Muhammad! Let those of your followers who have no accounts, enter through such a gate of the gates of Paradise as lies on the right; and they will share the other gates with the people." The Prophet further said, "By Him in Whose Hand my soul is, the distance between every two gate-posts of Paradise is like the distance between Mecca and Busra (in Sham)."
Helped you by highlighting it. The thing is many people fall in this trap and hope that their Prophets will intercede for them. The technicality of that is explained in the above Hadith. But even with Muslims, it becomes so much that their focus steps aside from fearing Allah in a guarantee that they'll be interceded by Prophet Muhammad (pbuh). Well, this verse clearly says, that Christians who belong to time period after Prophet Muhammad (pbuh) should upgrade, and this verse says, the Christians before the time of Prophet Muhammad(pbuh) who believed perfectly and did righteous good deeds, they need not go for intercession at all, because Allah is well pleased with them already.
Now coming to your question,
Does Jesus have the right and authority to intercede on our behalf, and is it ever acceptable for a Muslim to seek such from him (instead of, or in addition to, Muhammad)?
From the above explanation it is clear enough Jesus (pbuh) no more has the authority of intercession, next, is it ever acceptable for a Muslim to seek such from him, for a Muslim, it is never permissible for him to seek intercession from any of the Prophets(peace be on'em all), because it is clear Shirk. The concept of asking/seeking intercession from our favorite Prophets happens on the day of Judgement, not before it. Plz note that, as long as you're alive, you will not find any protector, helper etc besides Allah.
May the creator guide us all.