Twitter – way to filter out retweets

The answers so far will only give you at most 100 retweets. There is an API method that returns up to 100 entries of a cursored collection (so you can page through it to get more), though.

There's more information on the Twitter Developers site at GET statuses/retweeters/ids, though you'll also want to read their page about Using cursors to navigate collections.

Edited to add: That said, the first thread on the Developers site that surfaced in a quick google has @episod, a Twitter employee saying:

You can't likely get to all of them. The data is spread out. Your best bet is to use the REST API to determine many of the users who performed the retweet, but the data will still be constrained.

It's easiest to track retweets as they happen rather than try to find them from the past. Use the Streaming API for that.

^{Source: how to get all retweet of a given tweet}

The Twitter web site will only show you the Tweets (and re-Tweets) of people you are following directly. The only exception to this is if the Tweet starts with @username and you are not following username then you won't see the Tweet.

So in your examples you should see Tweets 1 and 5. All the others will be hidden from you.