Dynamic URL Based on Relationships
To answer this you need to think about what you want to have happen when EE sees a URL - only with this clear can you work out what the right approach would be. So with your example, it sounds like ...
Redirect a URL and remove a segment
I actually just figured it out with an htaccess RewriteRule. RewriteRule ^blog/detail(.*)$ /blog$1 [NC,R=301,L]
Template Routes help and tutorial
You can start from this Mike Boyink's tutorial it is very clear and help me to understand better templates route
Resource router hijacking all template groups
:url_title will match any string that could be a url title as it is converted to ([^/]+)  To stop this rule matching template groups, you can check that the match is for a real entry in the ...
Use template at root directory using Template Route Manager
I don't think you can. You also don't need to do that. The template file you are wanting to be your homepage is already called index. http://www.ee2docs.com/cp/design/templates/new_template_group....
Remove all URL-segments except for url-title?
Whether you can depends somewhat on how your site / templates are designed. As far as EE is concerned, you don't really need to specify which channel or anything to retrieve an entry - the url_title ...
How to use segment_1 dynamically?
You have lots of options, which is best will depend on what your site design / data looks like. The following suggestions are not in a recommended order, just trying to separate out your options: ...
Problem with Template Routes and Pagination
This turned out to be a bug, which appears to have been around since 3.4.0. Temporary fix ℅ Ellis Labs is to replace the static segment 2 element with regex to achieve same end: no idea why it works, ...
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