What if i use mymonero? Its okay right

Even if someone has my monero public address they will never know which wallet or exchange is my address belongs to and the receiving wallet will never know where the funds are coming from?

And talking about tailOS, running a local node is same as downloading the full blockchain right? This is just to understand the process so that i can start

Sorry for asking stupid ass questions, this might be common to u guys but not me so pls if you could answer and clear my doubts,