On the first issue - that looks like the old IE 6.x mixed-mode security warning, a lot of sites (including some of guh-oogle's services and some of M$FT themselves lol) will throw those. If you have IE 6.x installed, upgrade to 7 or 8 and you _should_ stop getting those. If you already have IE7 or 8 I don't know why the frack you're getting those.
Second issue - I've never gotten twitter login prompts, are you trying to post to twitter? Every so often I get the windows security login, it's something set on the site you're trying to post to, just click cancel and move on. It's not an accessible target if its got that on it.