Wouldn't this kind of use go against bing terms of use as they probihit using the results for any kind of machine learning training?

> [Do not] Use data received from the Search APIs as part of any machine learning or similar algorithmic activity. Do not use this data to train, evaluate, or improve new or existing services that you or third parties might offer.

https://docs.microsoft.com/en-us/azure/cognitive-services/bi...

Note: I'm partly asking this because some time ago I was thinking of setting up a little bit similar thing and I decided it would go against bing api terms.

Why would it need to share client's IP address when it can just proxy it? Unless it is doing search queries directly from the client?

Same as DuckDuckGo then.