What’s the best way to hide a tab in a TabNavigator

You should take a look at the SuperTabNavigator component from the FlexLib project:

• SuperTabNavigator example
• SuperTabNavigator documentation
• FlexLib Component list

If you don't want all of the tabs to have close buttons (I understand from the question that you don't) it looks like you could use the setClosePolicyForTab() method for specifying which tabs you want to have them.

I've got a project with styled tabs (I assume you mean the tabs themselves, and not the content). I'm sure there's other ways, but this is what I seem to have ended up with:

.myTabStyle {
    tabStyleName: "myTabs"
}
.myTabs {
    backgroundColor: #ff0000;
    fillColor: #000000;  /* this is the tab widget itself, not the content */
}
<mx:TabNavigator ... styleName="myTabStyle" .. >

There's several places in Flex where you have to use CSS styles to refer to other styles to drill into the widget you want (another example is setting the titlebar style on a TitleWindow).

I hope this helps.

By the way, I've seen occasional "tearing" on Mac & Windows, FireFox, IE, Safari, Flash 9 and 10 with large fonts & colored tabs--I'm not sure if this something I'm doing, something about the larger fonts, or the colored tabs themselves--but just a heads-up. This only happens when building with the Flex 3 SDK (never saw it with Flex 2).