It's so confusing that "zij" is "she" or "they," and "zijn" is "his"! Maybe complaining about it will help me remember.
I thought it was as well but once you start to understand the relationship it becomes quite easy. It is the context and subject (singular vs plural) that will help you determine these. If 'hebben' follows Zij would be plural and thus be 'they'. If would see "Heb zij' heb being used for singular, then you would know 'zij' would be 'she' as in "Does she have..." versus "Hebben zij" (Do they have).
You will also find there are many words in the Dutch language that can be confusing, such as weer & staat.
I hope this helps.
How can we know the "zijn" in this sentence means "his" or "its" without the context?
I guessed it implied NUMMER as TELEFOONNUMMER. So obviously it couldn't refer to an inanimate object...
Number, doesnt only means phonenumber, but also a lot of things like serial number, license number and more
In English "I have [person]'s number" can mean that you see through them; is it the same in Dutch?
No, that's not the same in Dutch. This really refers to a number, most likely a phone number, but in specific contexts it could also be a student number, an employee number, a social security number etc. etc.