"A boy plays and falls."
Translation:Knabo ludas kaj falas.
Does "ludas" refer to play as in playing an instrument or as in playing a sport or both?
"La knabo" means "The boy". "Knabo" means either "Boy" or "A boy". By adding the definite article La, you've added the word The.
Basically, it changes the meaning from a generic boy, doesn't really matter which, to a specific boy, that one over there.
Because Esperanto does not have any indefinite articles.
un does not exist in Esperanto.
Now I can confirm that Duo ludas kaj dormas and “Ĝi falas kaj dormas” doesn't mean “It is falling asleep.”. :c
Because it's not correct. The simple answer is it's not grammatical, which you can tell without even knowing the vocabulary. In the English, "plays" is a verb, but in your translation you are using a noun, since any word ending in -o (or -on, -oj, -ojn) is a noun.
More specifically though, teatro is a theater, and teatraĵo is a "theater thing" or a play/theatrical production, so teatraĵojn is theatrical plays as a direct object of a verb; and the only verb you had was falas.
"iu" is "some". Not as in "some (random) boy", which I think is idiomatic English, but as in the partitive. Since "boy" is a singular discrete noun, that wouldn't be grammatical. Also, Esperanto does not have the equivalent to "a/an", so just "knabo" would be "a boy" or "boy" depending on what is appropriate for the English translation.
If you're referring to the lack of indefinite article in Esperanto, then yes, it's like Welsh or Irish in that regard.
IIRC, noun + -n is the accusative. E.g. “Ni amas vin.” (We love you.)
That is correct. The -n noun (and adjective) suffix is for the object of transitive verbs.
I thought if you already had a verb in a sentence the rest had to be an infinitive.
That's only when they're working together, as in "He learns to read". Here, the two verbs are separate: A boy plays. A boy falls. A boy plays and he falls. A boy plays and falls.