Do you mean like Google Search Console? They have Bing Webmaster Tools that have many reports including search keywords, SEO reports and much more.

Yes, and it's fairly common. Each of the search engine may or many not use your meta title. If the search engine deemed that another title (derived from the laning page) will match the user's intent better, they may switch it.  Since Google & Bing have different algo's, this happens. For more info see How Does Bing Choose The Title For My Web Page.

Many ways to do this. I recommend getting a VPN/Proxy (I use Windscribe) to connect via IP address from US and use incognito mode.  There are third-party services that can do it as well. Good luck!

Do keyword/competitor research and create compelling content that is great link bait. Inbound links will organically occur if the content is useful. Repeat this many times and traffic will increase for these landing pages and push your DA up. It's difficult, and requires much times/resources. This is a better route than buying links that can get you hurt you in the future. Good luck!

There are many tools that do this. However, I would suggest staying away from them. Spend that money on create valuable content for the users. There will be a better long-term roi and the risk of getting a algorithmic or manual action taken against your site is greatly minimized. Good luck!