(moving to Developer Teatime as this is not a Streaming API question)
Please do not build a crawler that scrapes Twitter’s HTML. This is specifically against the Twitter Terms of Service and the Twitter Rules, both of which you agreed to when you signed up for the service.
Take a look at developer.twitter.com as a starting point with the API.
If an account is public, you can fetch up to 3200 of the most recent Tweets using the user timeline API. If the account is protected, you would need the user to authenticate through your app via the OAuth endpoint to grant access to the timeline endpoint.
For access to additional data, unfortunately you’d need to look into one of the enterprise data products, which is unlikely to be suitable for you as a research project.