Neatweet doesn't deal with twitter's basic api (so we never get to see your password, it's a good thing), it deals with the oauth system for your peace of mind.
When you sign in to this website you do so with cookies and background magic. These cookies aren't transferrable to your twitter client, and the magic just doesn't work outside of this site.
Because your twitter client is going to need to authenticate with us (again, a good thing) we need to get a password from you to store against the magic and cookies we use to talk to Twitter on your behalf.
We take passwords seriously here, when you give us a password we take that password and run a whole bunch of math and algorithums on it to turn it into a non-reversable encrypted hash - specifically we perform Salted SHA1 on your password.
Your password can never be recovered once it's been hashed. This helps us sleep better at night
No.
In case you missed that: NO!
The whole point of using oauth on the website is to that we never see your twitter password, so we can never take control of your twitter account, and so that you can easily manage our access to your twitter feeds from the connections tab in your twitter account.
It's really quite easy, you change the username you're using to include the filter. An example will make this easier to explain
So, for exapmle your normal twitter username is "fred", and you have created a filter with the name "work", the way you tell your twitter client to use that filter is to change your user name to "fred^work". Simple!
Neatweet does support SSL, however it's a touch confusing, as this service is hosted on Google's Appengine which does not directly support SSL on domains.