Translation:My uncle smokes twenty cigarettes a day.
Would this sentence still have an equivalent meaning if the "po" were removed, as "tage" can already mean "daily"...?
I don't think so. Tage means dum la tago. en la tago or dum la taglumo and therefore Mia onklo fumas dudek cigaredojn tage would mean “My uncle is smoking twenty cigarettes during the day”. Maybe the difficulty arises from the fact that English decided to use the word “daily” to mean “every day” and not “having the nature of the day” (as it happens, the ending “-ly” can go either way). I guess you could use ĉiutage to translate “daily” and say Mia onklo fumas dudek cigaredojn ĉiutage though.
Ne eblas. "po" is something like "to each one ..." or "... each" -- "Ŝi donis al la knabinojn po ses fragoj" = "She gave the girls six strawberries each"
So "po tago" would mean "to each one, one day" or "one day each".
But you are counting cigarettes per day, and not days per something - so it has to be "po dudek cigaredoj" (with nominative after the preposition "po").
(Or, for advanced use, "cigaredojn po dudek" or "po dudek cigaredojn" -- "cigarettes, twenty each".)
It's a tricky preposition that doesn't really correspond exactly to anything in English.
It's something like "... each" or "... apiece".
"Li donis al la knabinoj po tri pomoj" = He gave the girls three apples each / He gave the girls three apples apiece / He gave each girl three apples.
So it kind of distributes a larger number by saying how many of that larger number go to each something.
"La ĉambro kosts po dudek dolaroj nokte" = The room costs twenty dollars a night / The room costs, every night, twenty dollars each? This one is trickier to rearrange. But you're basically distributing a bunch of money among nights and for each night, it's twenty dollars = po dudek dolaroj.
The confusing thing is that English puts a preposition or article before the number of "recipients" (three times per week, twenty dollars a night), but Esperanto before the quantity that is being distributed (po tri fojoj semajne; po dudek dolaroj nokte).
"po" is indeed a preposition - the question is what it governs.
The most basic use would be something like "po dudek cigaredoj", where "dudek cigaredoj" is the complement of the preposition "po", and is in the nominative.
But you could also say something like "Li fumas cigaredojn, po dudek tage", with "cigaredojn" as the object of "fumas" (and thus in the accusative) and then "po" only in front of "po".
And that sentence could be rearranged to "Li fumas po dudek cigaredojn tage"... with "cigaredojn" still the object of "fumas" and "po" governing only "dudek". But it's a bit confusing to say the least.
Even "worse" is if he smokes 365 cigarettes a year, but only one a day -- then it would be "Li fumas po unu cigaredojn tage" if you wanted to use that word order -- because it's equivalent to "Li fumas cigaredojn, po unu tage" (he smokes many cigarettes, but only one each day).
"Li fumas po unu cigaredo tage" is, I'm sure you'll agree, quite a bit clearer.
Komparata al mia patro, la onklo estas preskaŭ nefumulo.
Mia patro mortiĝis pro tro da fumado.