Are you using Internet Explorer? TweetBeaver doesn't support Internet Explorer so while the site will work, you're better off with Chrome, Firefox or Edge.
Frequently Asked Questions
TweetBeaver accesses Twitter data through the Twitter API which requires authorization in order to limit the number of searches made by each user. When you sign in, Twitter authorizes your account to make those searches through TweetBeaver.
No, the whole point of the sign in with Twitter process is that you don't have to give third party websites and applications your login credentials. When you sign in, Twitter checks your credentials then passes access tokens to TweetBeaver to give you access. You can revoke access in the settings page of your Twitter account.
TweetBeaver will never post to your account. Twitter applications have three permission models (read only, read/write and access Direct Messages), each with different capabilities. Some of TweetBeaver's functionality requires the read/write permission level despite never needing to post tweets on your behalf. One of the calls TweetBeaver makes is users/lookup which is recommended to be a POST for large requests. TweetBeaver does multiple searches of 100 (the maximum) at a time. Any API method that requires HTTP POST is considered a write method and requires read/write access.
Twitter limits the number of requests you can make to its API to prevent abuse. Details of rate limits are here.
These limits are put in place by Twitter.
Not in the near future. I've been developing TweetBeaver for a while now and still have lots of ideas for new tools but am not currently in a postion to develop it further. But if you have any ideas of useful tools you can email firstname.lastname@example.org and it could become a project for the future.