Very few mics have suppression by themselves.

With the mic itself, you can be careful not to have too much gain, so that it does not even perceive a part.

Then, during the recording, you can use software to cut out background noise. On the one hand, you can use a noise gate so that nothing below a certain volume activates the mic, and on the other hand, you can process the recording with noise filters.

Depending on the type, there may already be active noise filtering that can be activated. With PulseAudio (Linux), for example, you can activate this and the result is amazingly good.

No, it will not filter the background noise. But if you speak 10-15 cm close to the microphone, then the background noise is, by principle, less audible. At least, if it's not a hoover. Therefore, a microphone arm or something similar would be recommended.

Not quite sure, but it has excellent sound quality, especially when you are close to it.