handling login authentication with ajax for OSX dashboard widget?

Question

I'm wanting to build a simple OSX dashboard widget to tie in with my web application.

The widget will need a login screen first (user and password) to use it though (checked against user table in hosted mysql database, password stored SHA1 encrypted)

So my thought is that the widget will need to:

• show username and password fields

• Pass the input to a remote php script that will check it against mysql table

• Pass back sucess / ok to use widget functions or failure

My questions:

1. If login success, is there anyway to remember / stay logged in? or does happen automatically.. until the user closes the widget?

2. Is there anything I can do to make the passing of login information to my remote php script more secure?