I suppose a literal translation may help. As a native speaker I never have to learn the grammar so I cannot help you with that.
"He should have arrived by now."
他 > He
这个 > this
时候 > moment / time
该 > should / should have
到 > arrive (Not "arrived". Recall that Chinese doesn't have explicit past tense, or any tense at all.)
了 > have / already (Indicate completed action of "到" i.e. "arrived" but modified by "该")
But then of course plenty of questions about "了" have been asked on this site. Please do a search for more academic answers. For example this has similarly been answered in this question: Why can't 了 be used to complement 到?
Answering your side question, "了" (and its counterparts) is used a lot in conversations. In addition to the other answers about "了" on this site regarding its literal meanings, it is often overused in daily conversations somewhat like "Hmm", "OK", "I mean" in English (bad analogy I know). Has meaning, maybe redundant, but often unnecessary. Doesn't make it incorrect usage though. Like when you learn about "兒", it is being used (to the extend I would say abused) in the North with no apparent meaning. TBH old Chinese (文言文) is way more efficient (and elegant), though it can be difficult to comprehend without context.
As a side note, the usage of "了" in your example provided is similar to "啦" in Singlish and "咗" "喇喎" in Cantonese.