Questions about authorship rank and academic politics
I should point out one of the most famous of co-authors in math: Paul Erdős. Erdős never won a fields medal or even wrote a seminal paper as a solo author. What he did do was "wander" around to different universities and help people solve problems. He was an extremely prolific writer (over 1500 published manuscripts) and is considered one of the greatest mathematicians of the 20th century. The ultimate mathematical Renaissance man who could seemingly work on any problem.  I think you would have quite a bit of difficulty in arguing that because Erdős never wrote a classical mathematics paper as a solo author, he was not a tremendous mathematician. (Though to be fair, in the past decade, his paper "On Random Graphs" can now be considered a classical work of mathematics. It just took 50 years for the work to become highly applicable). 

I relate this story because having lots of co-authors does not necessarily mean having bad skills. Now I am not saying your professor is the second coming of Paul Erdős (I can't think of anyone currently in academia who can claim that mantle) but they might have other skills you are not giving them their due credit for. 

Never underestimate the power of being able to organize a group of smart people and get them to work together on the same problem. 

To answer your questions specifically-


It's neither normal or not normal. Tenure positions are rare enough that there are certain metrics that are highly predicative (e.g. individuals who are ahead of the publication curve for their field tend to get hired in tenure positions) but there is no conclusive metric. Individually, there is enough variance within each position that you cannot really say. 
Collaborate! Having only solo author publications is probably not wise (unless you are in a field that is big on monographs). Having a variety of publications where you are first author, second author, and a middling author show your ability to collaborate and be a team player. 
Yes, clout does increase likelihood of getting accepted. Being a big wig with 10,000 citations at an elite university means you are more likely to get a grant than someone with a handful of publications from an R2. But to be fair, the qualities that led that person to be a big wig probably translate into their writing and research caliber as well. 
I have never seen any research or evidence that suggests that.