Yes, if you skip the template name and put an EE recognized segment in there (category ID, url-title, etc) EE will assume the index. Before the Pages module I used this to display entries at /info/about etc - where about was the url-title and info the template group, no template name.
C1 isn’t a parameter, it’s a segment, but some segments EE handles automatically. You do need to have that information in the segments for some operations but not all. I don’t know what you mean by “weblog_archive” so I can’t answer that. If you mean the category archives tag, that does not require a specific segment type.
If you use the {exp:weblog:entries} tag without dynamic=“off” then EE will restrict to what is in the URL in segment_2 or segment_3. If that is a url_title then it will show only a single entry and any comments/comment form you have shown. If it’s a category ID then it will limit the list of entries by that category; or if you use category names, then if it’s the trigger word you chose.
You don’t need the code in the template, it is a combination of the weblog entries code and your URI segments.
So, put this into a template:
{exp:weblog:entries limit="10"}
{title}
{/exp:weblog:entries}
Now, visit it at just that template - it’ll show you the last 10 entries. Append a category id like C1 and it will show the last 10 entries in category 1. Append a url-title and it will show you only that entry.
Make sense?