Pulling #hashtags and displaying them on site
This is possible using the dev branches of a few modules put together:

feeds, >= 7.x-2.0-alpha8+56-dev

feeds_oauth, >= 7.x-1.0-beta3+2-dev

feeds_jsonpath_parser, >= 7.x-1.0-beta2+12-dev

I think there are a few other necessary modules you'll need to have installed, like oauth, ctools, feeds_ui.
One of the most important things is that you need to register an app at dev.twitter.com, and get an API key / secret. You put that into the feeds setup (admin/structure/feeds/FEED_NAME/settings/OAuthHTTPFetcher). When you setup your feed, you will want to choose the HTTP OAuth fetcher (oauth2 does not work) as the Fetcher type.

You create a new feed importer.

Additionally, you'll want to create a content type like "tweet" and add the fields you want to parse (like author, date, name, body, location).

Back in the feeds setup, setup your mapping, and create several jsonpath_parser maps to your respective fields. After that, click "settings" under JSONPath parser, to map your json contexts to your fields.

It should be something like this:

Context: $.statuses.*

Title: id_str

body: text

etc, etc, etc

Finally, once this is all setup, you can go to SITEURL.com/import
and input your search string, which will look like this:

https://api.twitter.com/1.1/search/tweets.json?q=%23HASHTAG

Anyway, I hope this is helpful. I realize that my answer could be better organized, but it should give the gist as to how this is done.

For my "tweet" content type, I have the default setup to be NOT published, so that I can moderate what actually shows up on my site.

One more caveat is that non UTF-8 strings (common in foreign languages for example) will error out and break your feed importer (which should run on cron automatically). Ideally you want to sanitize the input before writing it into the database anyway.

Here's the PHP you can put into a quick custom module to sanitize the input of the body field for example. You want to make sure your jsonpath_parser:ID matches the ID you setup in the node-processor settings.

&lt;?php

/**
 * Implements hook_feeds_after_parse().
 */
function feeds_custom_feeds_after_parse(FeedsSource $source, FeedsParserResult $result) {
//dpm($source); // look at source variables, requires devel
//dpm($result); // look at result variables, requires devel

  foreach ($result-&gt;items as $delta =&gt; $item) {
    $result-&gt;items[$delta]['jsonpath_parser:1'] = utf8_encode($item['jsonpath_parser:1']);  
  }
}