It is. BTC itself isn't 100% anonymous honestly speaking, but you can ramp up the anonymity factor through various methods. For example, P2P exchanges like LocalBitcoins don't require any form of KYC(Upto a certain limit).
It's still better to just comply instead with these exchanges terms instead of using non-popular exchanges where the chance of getting scammed or being treated unprofessionally has a high chance.
That depends. If you want complete anonymity, it is still possible to trade crypto without submitting KYC through exchanges like LocalBitcoins etc. If not, it's better to comply with centralised exchange requirements as you mentioned.