Hi Sydney,
For 1), I'd recommend the Twitter report which you can access via the "Generate Reports..." link. Once you've selected the Twitter report, you'll see options in the left pane. You can Filter Data to specify the node sets for which you'd like to get measures back. For example. if you choose the networks using hashtags, tweets, and agents, you'll get back various rank and centrality measures for the hashtags and agents nicely formatted in the html reports. That should give you a lot of data about the key agents and hashtags.
2) You can click into the tweet nodeset editor and search for the hashtag in the search box above the grid and beneath the menu options. That will display just the tweets with that hashtag and you can view them there. You can copy and paste the grid into Excel or a similar application if you'd like to save them. I've highlighted where to click for the option to copy the grid:
Hope this helps,
Dawn Robertson
CASOS