Must be a school class on a trip to the senate... Now, really, these are strange sentences. They do help you to learn, I give them that. In order to help out, I created some more meaningful Latin sentences: Psittacus ebrius militem mordet. Ergo, miles iratus Psittacum coquit. Postmodum, milites laeti cum puellis impiis noctem prodigunt. Here we go. Everything is back to normal. The earth travels in an ellipse around the sun again.
No, because that would be: Senes perfidi pueros numerant. The only ambiguity in the sentence is the word “senes” because, in the plural, it is identical as both subject and object. (Here it is the object.) Roman writers generally resolved ambiguity with word order, as in the sentence we are discussing: subject-object-verb.
Because my native tongue is Portuguese, I find accusative is the easiest case to spot. The plural of the first two declensions ends in '-os' or '-as', which are the plural forms in Portuguese (and Spanish).
In this case, then, 'perfidos' is readily apparent as an accusative and so it is the object. Since 'pueri' is in the nominative, there should be no ambiguity that it can apply only to 'senes'.
And for that reason too, 'senes' has to be in the accusative and so there is no ambiguity at all in this phrase, at least that I can see.
-- add on/edit change -- // per Wiktionary, apparently what I wrote below about the middle syllable of "perfidus" having a long vowel was mistaken, sorry -- //
I just used the "report" button re "the audio sounds wrong" -- for what it's worth, the audio for this sentence (today 29 Sep 2019) is not differentiating much or any between short and long vowels, and hence has the syllable stress wrong on perfīdōs -- senēs perfīdōs -- I've noted the like in many other audios, and I think others have commented about it also -- correct vowel and syllable length are vital for Latin poetic meters, and I think thoroughly appreciating Latin poetry in the original has long been one of the principal reasons people have aspired to learn the language, and still should be now --
As you have said, you were wrong about the length of the i in perfidōs, but otherwise I think you make a good point regarding vowel length in the audios. I listened to this sentence several times, and in particular thought that perfidōs sounded more like perfidus. I have reported this as "The audio does not sound correct".
-- in traditional grammar terminology from my school days, I think "senex" = "old man" is a 3rd declension consonant-stem noun -- I think the singular case forms nom/gen/dat/acc/abl go thusly: senex senis senī senem sene -- and the corresponding plural forms go: senēs senum senibus senēs senibus -- "senēs" would be the correct form for accusative plural --