Can you include a link to the test results? In the meantime I can provide some generic guidance:
a - The connection view shows each TCP socket and the requests that are retrieved over them. If persistent connections (keep-alive) isn’t enabled you’ll see a bunch of different connections with only one request on each. The most basic site that serves everything from it’s own domain (with persistent connections enabled) will have 2 connections (6 for IE8) that all of the requests are retrieved from. Here is a sample: http://www.webpagetest.org/result/090707_1TK1/1/details/
b - Not sure I understand the question. Do you mean they are not all showing connection time but are showing REQUEST time? Only the first request over any given connection will have a connection time (the socket is already connected for the rest of the requests). All of the requests need to make a round trip for the request itself though.
c - You can reduce the number of connections by enabling persistent connections/keep-alive. Beyond that you need to reduce the number of requests which means combining js/css files, image sprites, etc.
d - The only way to reduce the connection time is to get your servers physically closer to the customer. The connection time is completely driven by the round trip time from the customer to your servers. Usually this is done by using a CDN which can distribute your content to hundreds of servers around the globe. Usually the impact can be reduced by first eliminating as many requests as possible and seeing if it is still worth the $ for a CDN after you have optimized the site.