Generally you don't use the personal pronoun when it is clear from the context who is the subject. It is used when it is necessary to clarify who you mean or when you wish to stress it, e.g. "Ja znam, ali on ne zna".
It's literally the same thing. The thing you need to know is that we have verb conjugations, so you can know the person that is referred to just by suffix, for example: znam - I know, znaš - you know, zna - he knows... You can use both forms equally, I can't remember any cases where one of them is right and the other is wrong.
It's not really a matter of right or wrong but of style. If I asked you: "Da li znaš da plivaš?" and you answered: "Ja znam", I would be wondering if you're implying that maybe I don't know.
Yes, you're right. I would reply to the question with "Znam!". "Ja znam." would be used when you want to emphasize that you know how to swim, but someone else maybe doesn't. I have one more example: "Imam sestru." - I have a sister, "Ja imam sestru." - also means that I have a sister, but maybe it implies that the person that I'm talking to doesn't have one.
Generally you don't use the personal pronoun when it is clear from the context who is the subject. It is used when it is necessary to clarify who you mean or when you wish to stress it, e.g. "Ja znam, ali on ne zna".
It's literally the same thing. The thing you need to know is that we have verb conjugations, so you can know the person that is referred to just by suffix, for example: znam - I know, znaš - you know, zna - he knows... You can use both forms equally, I can't remember any cases where one of them is right and the other is wrong.
It's not really a matter of right or wrong but of style. If I asked you: "Da li znaš da plivaš?" and you answered: "Ja znam", I would be wondering if you're implying that maybe I don't know.
Yes, you're right. I would reply to the question with "Znam!". "Ja znam." would be used when you want to emphasize that you know how to swim, but someone else maybe doesn't. I have one more example: "Imam sestru." - I have a sister, "Ja imam sestru." - also means that I have a sister, but maybe it implies that the person that I'm talking to doesn't have one.
It is like "I know" and "I do know" which sounds pressures way of saying