No, you cannot. Chrome has not been ported to Windows Phone in fact it hasn't been ported to iOS either. Google Chrome on iOS is not nothing but Safari with a different theme and some extra features (Chrome history/tab sync).
Google Chrome so far has been really ported to only one mobile platform, Android.
Note that, porting Chrome to both iOS and ...
Well, there is no such a restriction with browsers on Windows Phone. UC Browser is quite nice choice for example. But since there is no Chrome on Windows Store, the answer is no. Unless you want to search for some custom app which is available somewhere in the web, but you're going to need developer unlocked phone for that.
There's no official Stack Exchange app for Windows Phone that I'm aware of.
However, fellow WPSE user RareNCool was earlier this year developing an unofficial app. Last I checked, it was in closed beta. See this meta post for more info and instructions on how to get into the beta.
No, there is no support for Flash. Flash is an outdated technology that no-one should support. If you find a website using Flash, please ask them to convert it to HTML5 instead.
Regarding RTSP, no, there is not.
Update : For some pages Refresh or Clearing cache does not reset the zoom level. For those website click on the location bar and press Enter key or Left arrow that appears in the keyboard.
Clean the cache and cookie data in Edge. However it must not be necessary. Edge resets the zoom level to default when pressing refresh button.
The browser also "...
Not to my knowledge.
The reason it keeps suggesting an app is due to the way Edge is coded. It's coded to request the android version of web pages. The page detects a request from an android device, and includes the code to advertise their app and open the Play store link.
Unfortunately you cannot currently do this. The settings page you mentioned is so that apps can handle links related to their function (e.g. Readit might handle reddit.com or myTube might handle youtube.com). This does raise the question of whether or not an app could register itself to simply receive, for example, http://*, but unfortunately I don't have an ...
If you go to Settings => Easy of Access => Font Size and increase the font size there, built-in Internet Explorer will respect this and increase font size of web pages. It works this way on Windows Phone 8.1 for my Lumia 920.
To see your bookmarks in Opera mini on Windows phone follow these steps
Open opera mini
Click on the hamburger icon located at the bottom.
You should see the bookmarks icon on the left side.
Click on the icon and you can see the bookmarks.
As this is still one of the most requested features on Windows Phone UserVoice I assume it is not yet possible or at least no one has tried to create browsers with rendering engines different from Trident. This might be due to the limited API access for native code. So Opera Mini and all the others are propably wrapping around an IE webview, yes.