We wouldn't say "the 1" in English to refer generally to the number one. But as you see if 1 were preceded by the word 'number' then you would say "the number 1" to generally refer to that number. When you say "the 1" that would mean you are referring to some specific 1 of something. It sounds pretty weird actually. As an English speaker I would think you were trying to make some kind of joke or trying to be clever about something.
I know 1. (Equals I know the number one (the general number 1 we use to count or it can mean I know of one of whatever is being discussed.)
I know the one. (Equals I know of the thing you are discussing; this does NOT refer to the number 1.)
I know the number one. (Equals what it sounds like.)
I know number one. (Equals I know the first one of the things you are talking about or if capitalized could mean you know somebody or something who/that has been given the title Number One such as the Captain Picard's first officer on the Enterprise.)
I'd guess because the arabic sentence does not use the definite article? I've observed that arabic uses "ال" in some instances where the english translation does not use "the", but I don't recall any instances where english includes "the" when the arabic translation does not use "ال". (I'm still learning, and may easily be wrong about this)
lakinna لَكِنَّ can't be followed by the verb directly. But, we can use lakin لَكِنْ. If we insist on using lakinna لَكِنَّ, we can write it as lakinnanii لَكِنَّنِي or lakinnii لَكِنِّي (means: "But, I")
لا أعدُّ كثيراً لَكِنْ أعرفُ ١
لا أعدُّ كثيراً لَكِنِّي أعرفُ ١
لا أعدُّ كثيراً لَكِنَّنِي أعرفُ ١
Not in this context. The english sentence appears to mean "I do not count often (so I am not very good at counting, and don't know most numbers), but I know (the number) one".
Glossing "a lot" as "many" would mean you are (avoiding) counting a large number of things, and would make nonsense of the "but I know 1!" part.
In this Duo sentence, you could use "much", "often", or "frequently" for "a lot", but not "many". "Many" would only work for "a lot" if you are referring to the number, and is not an appropriate substitute for "a lot" when referring to the frequency.
(but that's just from my knowledge of english - I don't know whether كثيرا has same variety of uses that a lot does. And I know that expecting a Duo sentence to avoid nonsense may be unrealistic. Maybe that's what the author was doing for?)