Yes. If you are simply walking around with your camera and shooting casually, you generally do not need a permit. You will, however, need a permit if you are filming on public property such as a police station, OR if your filming impacts others and/or the environment.
It is almost always lawful to photograph people in a public place without their consent.
However, you cannot film or take photos of people if they are in a place where they can expect privacy, such as their home, a public changing area, or a toilet.
Moreover, if you follow someone or a group and continue to film them, after a while, they can have a claim against you for harassment or even disturbing the peace or even stalking. The situation is different if you are on private property like someone's house. There, the owner sets the rules. You cannot film if the owner does not want you to.
If you refuse to go by the property owners' rules, they can order you off their property (and even have you arrested for trespassing if you do not comply).
Police should not order you to stop taking pictures or video, unless instructed by the property owner.
As for recording audio, states have eavesdropping laws, which criminalize recording oral conversations without permission. This has led to numerous charges brought against those recording videos. This is particularly so since videos are almost always not silent. In order to get around these restrictions, try filming without sound.
It is not against the law to record your own conversations with others without their consent, be it face to face or over the phone, as long as you yourself consent to recording it.
However, it is illegal to record conversations between others that you are not participating in.