"Aamir knows my sister."
Translation:आमिर मेरी बहन को जानता है।
A transitive verb is, by definition, one that can take direct objects. But sometimes, we separate the direct object from the verb with a postposition को keeping the following pointers in mind:
को is always used when the object is a sentient noun. So, when talking about people, it's always आमिर को देखो, never आमिर देखो. Similarly, when talking about pets or ascribing a personality to animals, को is always used. But you can say मैंने एक भीड़ देखी (I saw a crowd) because the 'crowd' is impersonal though it may be composed by people.
This is why this sentence आमिर मेरी बहन को जानता है। has a को
For inanimate objects for which both forms are valid, the form without the को is the most natural phrasing but when को is used, you place some additional stress on the noun. This introduces a subtle change of meaning. For example, मैंने वह किताब देखी just means that I saw that book but in मैंने उस किताब को देखा, because of the stress placed on the object, it means that I saw that book with some deliberation. As a result, the second sentence is closer to 'I looked at the book'. With other verbs, this difference may not be as pronounced. For example, the only difference between यह क़मीज़ पहनो। and इस क़मीज़ को पहनो is that the latter is a more persuasive statement.
Note: This usage (placing it between a verb and its direct object) of को is very different from the other usage where it is similar to 'to' and must not be confused with it.
पता होना is not used in the context of knowing people. It is used mostly for facts etc that you know but there is no level of comprehension required. Eg: क्या तुम्हे पता है की मेरा बटुआ कहाँ है? (Do you know where my wallet is), मुझे उसका नंबर पता है (I know his number)
जानना is also 'know' but there is some level of understanding implied. Eg: मैं जानता हूँ कि मुझसे गलती हुई है (I know that I've made a mistake), क्या तुम जानते हो कि कल यहाँ क्या हुआ था? (Do you know what happened here yesterday?) etc. जानना can also be used to say that you know/are familiar with people or things. Eg: क्या तुम मेरे दादाजी को जानते हो? (Do you know my grandfather), मैं इस मंदिर के बारे में जानता हूँ (I know about this temple).
Yet another way to say that you know something is to simply use the verb आना (to come). This is used for skills, games or languages that you know (जानना can replace आना in most of these cases but using आना is often used to distinguish 'know the skill' from 'know about the skill' ). Eg: मुझे हिंदी आती है (I know Hindi), क्या तुम्हें क्रिकेट खेलना आता है? (Do you know how to play cricket), उसे गिटार बजाना आता है (She knows how to play the guitar)
Perhaps you're joking, but otherwise note that it's unlikely^ that abstract meaning of 'there' translates directly to वहाँ, there's no real reason for it to be the same word as the 'that physical place' use, it just happens to be in English.
^this applies more generally as something to watch out for, since it can produce such strange sounding sentences to native speakers(!) but specifically in the case of वहाँ, I'm pretty sure you can't use it like this.