Gør plads, for Prins Ali! [Make way for prince Ali]
Ban vej, for Prins Ali! [? way for prince Ali] - I don't understand 'ban' but there are a lot of results if you google 'ban vej for' where it clearly makes 'to make way for' - It does indeed mean make way for. It is the imperative form of 'at bane' 'to make (way)'.
Plads, giv os plads [Place, give us place] (Room or space would make better sense here. Place is 'sted' in Danish.) 
og gør vejen klar [and make the way clear]
hej, du! flyt dig nu for en superstar [hey you, run to (see) the superstar](move now for a superstar)
åh, stil dig et sted hvor du ser hans stråleglans [ah, put yourself in a place (or: stand somewhere. 'Stil dig' - stand (imperative form))where you (can) see his splendour]
Lad trommerne gå, en fyrste som få [let the drums beat (for?) a prince who] - I don't completely understand få here. ('Få' can mean 'to get'. Here it means 'few'. So the sentence is: a prince/ruler like few.)
kan opleves her til lands [can be seen in this land](or: experienced - kan opleves)
Prins Ali [prince Ali]
er et geni [is a genius]
Ali Ababwa [Ali Ababwa]
Buk korrekt [Bow correctly]
vis ham respekt [show him respect]
læg dig på knæ [fall on your knees]
din hilsen bør være varm [your greeting has to be warm]
et underdanigt "salaam" [a humble "salaam"]
mens du beundrer hans følge af folk og fæ [while you are admiring his train (following/entourage) of men and animals]('Fæ' is more like an idiot, so maybe the town idiot in this case).
Prins Ali [prince Ali]
mægtig og rig [mighty and rich]
Ali Ababwa [Ali Ababwa]
Energi med garanti [guaranteed energy]
styrke som ni [as strong as nine (men)]
tænk kun ved hjælp af sit sværd [(just you) think, only by using his sword]
slog han den fjendtlige hær [he beat the enemies' army]
hvem gav dem bank hver især? [Who gave them all a beating?] - I found only the verb banke - to hit, but this shoud be a set expression?..(At banke - to beat. At banke på - to knock (on a door))
Jo, Prins Ali [yes, prince Ali]
Han har femoghalvfjerds guldkamaler [He has seventy-five golden camels]
(Er det ikke flot, Ulla?) [Isn't it great, Ulla?] The English version of the song has June and Harry instead of Ulla and Paul. Those "Harry and June" are a parody of parade commentators.
og af påfugle har han halvtreds [and peacocks, the(he) has fifty of them]
(Jo, Poul, se de kostumer!) [Yes, Poul, look at the consumes (costumes)!]
Han har dyr helt besat med juveler [He has animals burdened (adorned) with jewelry] ('Besat' can also mean possessed)
hans samling er kendt [his collection is famous]
heæt eminent [??? brilliant(ly)] (Heæt is not a word in Danish. I just heard the Danish version and it is 'Helt eminent' - which means totally or completely brilliant.)
røse mus og ternede gæs [Haha, what sort of mice and what sort of geese? I don't get it but must be funny :))] (It is 'Røde mus' - red mice. 'Ternede gæs' - checkered geese :)
Prins Ali [prince Ali]
Sikke't parti [what a match!](I would go with 'what a catch' here)
Ali Ababwa [Ali Ababwa]
Den fysik [his (that) physique]
skaber panik [drives one crazy](creates panic)
sikken kemi [what a chemistry]
Kom med til byens basar [come (med: along) to the bazaar of the city]
ret sløret an og gør klar [tidy your veil and get ready]
og se så et eksemplar [and see this phenomenon (specimen)]
se Prins Ali [see prince Ali]
han har femoghalvfjerds hvide aber [he has seventy-five white monkeys]
og entreen er fuldstændig fri [and entrance (to see them) is absolutely free]
han har slaver der bukker og skraber [he has slaves who bow and prostrate]
de elsker ham højt [they love him greatly]
lystrer hans fløjt [lit. obey his whistle? I'd say 'serve his whim'](or: obey his every whim. 'Lystrer' has the connotation of a dog obeying its master)
bli'r loyale til hysteri [stay madly loyal]
mod Ali [to Ali]
Prins Ali [prince Ali]
fuld af magi [full of magic]
Ali Ababwa [Ali Ababwa]
Jeg har hørt jeres prinsesse er så skøn [I heard your princess is so beautiful (or: lovely)]
og det er derfor at jeg [and that's why I]
tog prinsen med denne vej [took the prince on this way (or: took the prince here)]
med elefanterne [with the elephants]
lama'r i flok [flocks of lambs (lamas)]
leoparder, bjørne [leopards, bears]
og livvagter nok [and some (enough) bodyguards]
med horn der støjer, og papegøjer [with trumpets that are blowing (noisy) and parrots]
og festmusik i det fri [and celebration music in the open air]
gør plads for prins Ali [make way for prince Ali]

Interesting and good way to practice! :)

Gør plads, for Prins Ali! [Make way for prince Ali]
Ban vej, for Prins Ali! [? way for prince Ali] - I don't understand 'ban' but there are a lot of results if you google 'ban vej for' where it clearly makes 'to make way for'
Plads, giv os plads [Place, give us place]
og gør vejen klar [and make the way clear]
hej, du! flyt dig nu for en superstar [hey you, run to (see) the superstar]
åh, stil dig et sted hvor du ser hans stråleglans [ah, put yourself in a place where you (can) see his splendour]
Lad trommerne gå, en fyrste som få [let the drums beat (for?) a prince who] - I don't completely understand få here
kan opleves her til lands [can be seen in this land]
Prins Ali [prince Ali]
er et geni [is a genius]
Ali Ababwa [Ali Ababwa]
Buk korrekt [Bow correctly]
vis ham respekt [show him respect]
læg dig på knæ [fall on your knees]
din hilsen bør være varm [your greeting has to be warm]
et underdanigt "salaam" [a humble "salaam"]
mens du beundrer hans følge af folk og fæ [while you are admiring his train of men and animals]
Prins Ali [prince Ali]
mægtig og rig [mighty and rich]
Ali Ababwa [Ali Ababwa]
Energi med garanti [guaranteed energy]
styrke som ni [as strong as nine (men)]
tænk kun ved hjælp af sit sværd [(just you) think, only by using his sword]
slog han den fjendtlige hær [he beat the enemies' army]
hvem gav dem bank hver især? [Who gave them all a beating?] - I found only the verb banke - to hit, but this shoud be a set expression?..
Jo, Prins Ali [yes, prince Ali]
Han har femoghalvfjerds guldkamaler [He has seventy-five golden camels]
(Er det ikke flot, Ulla?) [Isn't it great, Ulla?] The English version of the song has June and Harry instead of Ulla and Paul. Those "Harry and June" are a parody of parade commentators.
og af påfugle har han halvtreds [and peacocks, the has fifty of them]
(Jo, Poul, se de kostumer!) [Yes, Poul, look at the consumes!]

Han har dyr helt besat med juveler [He has animals burdened with jewelry]
hans samling er kendt [his collection is famous]
heæt eminent [??? brilliant(ly)]
røse mus og ternede gæs [Haha, what sort of mice and what sort of geese? I don't get it but must be funny :))]
Prins Ali [prince Ali]
Sikke't parti [what a match!]
Ali Ababwa [Ali Ababwa]
Den fysik [his physique]
skaber panik [drives one crazy]
sikken kemi [what a chemistry]
Kom med til byens basar [come to the bazaar of the city]
ret sløret an og gør klar [tidy your veil and get ready]
og se så et eksemplar [and see this phenomenon]
se Prins Ali [see prince Ali]
han har femoghalvfjerds hvide aber [he has seventy-five white monkeys]
og entreen er fuldstændig fri [and entrance (to see them) is absolutely free]
han har slaver der bukker og skraber [he has slaves who bow and prostrate]
de elsker ham højt [they love him greatly]
lystrer hans fløjt [lit. obey his whistle? I'd say 'serve his whim']
bli'r loyale til hysteri [stay madly loyal]
mod Ali [to Ali]
Prins Ali [prince Ali]
fuld af magi [full of magic]
Ali Ababwa [Ali Ababwa]
Jeg har hørt jeres prinsesse er så skøn [I heard your princess is so beautiful]
og det er derfor at jeg [and that's why I]
tog prinsen med denne vej [took the prince on this way]
med elefanterne [with the elephants]
lama'r i flok [flocks of lambs]
leoparder, bjørne [leopards, bears]
og livvagter nok [and some bodyguards]
med horn der støjer, og papegøjer [with trumpets that are blowing and parrots]
og festmusik i det fri [and celebration music in the open air]
gør plads for prins Ali [make way for prince Ali]