Is it true that any current smartphone is broadcasting audio and position of its owner by design even if switched off and not given permission by the owner to broadcast?
This statement is not completely accurate.
The second part, "...and position of its owner...", requires the smart-phone to have a particular type of a gps tracking chip in it. This, I believe, is different than the usual "Turn on GPS so I can find my phone if I lose it" feature.
About the first part, "...broadcasting audio ... even if switched off ..."
This is possible under certain conditions. Short answer -- this does NOT happen.
What you are referring to is, basically, malware. In order for this malware to be installed on your phone, the following things need to happen:
1. The attacker needs a reason/motive to install it.
2. The attacker has to know the OS of your phone & have the appropriate software for that OS.
3. The attacker must have PHYSICAL ACCESS to your phone. (i.e. physically have it in his/her hand)
4. The attacker needs to have it unlocked & have a Cell-phone hub, capable of talking to your phone, available when it is physically available.
So, have you made anyone angry lately? Do you have any information that some-one else may want? Have you lent your phone to someone who has the equipment to do such a thing lately?
So, basically, you don't need to worry about it.
Note: Yes, I do know the source of this information. No, I cannot say.
The answer that can be relied on pretty much 99.9% of the time is 'no'.
For the audio part of your question: Probably some phones, somewhere, might do this if they are located in an area with an extremely nosy government. There is something they inadvertently agreed to that allowed their phone company to mine their data, or a government agency needs to spy on your phone for National Security. Also, your phone could be hacked. But no, about 99.9% of phones do not record your audio. It is an incredibly rare occurrence that they do.
For the location part: This is partly correct. While your ISP can track you as long as there are at least three strong signal towers that are capable of pinging your phone in the area, they do not track you unless a similar scenario to the ones mentioned above happens.
If you are truly so paranoid that all phones are out to get you, I have two possible solutions for you.
Solution one: disconnect from cellular data at all times, run a trusted AV at least twice a day( please do your research before downloading a random one off the internet), and when you use wifi, only use trusted networks and configure your phone to route all your traffic through Tor.
Solution two: Destroy your phone with a hammer (please don't)
When your phone is off, the same answer applies. People can still track you and record your audio, but it is EXTREMELY unlikely and quite difficult.
Assuming your phone is off: For most phones, some core functions will continue until the phone is powered off. If the hacker's attack is sophisticated enough, they will be able to exploit said features into gaining privileges to use the microphone, thus recording audio. However, as long as you are disconnected from wifi and cellular, the attacker will not be able to use any information they have exfiltrated until you regain some sort of internet connectivity.