<1> Unsure about the button in previous versions, as I don't have SAM in front of me.
<2> File | Export Audio will work for mixdown, but if memory serves -- and if SAM 11 is similar to previous versions -- it doesn't provide as many options, for example with respect to sample rate conversion, as Track | Bounce (Mixdown). Or, at least, Export Audio provides different options. Try Track | Bounce (Mixdown) on the main menu (or something close to it such...don't have SAM in front of me, but Bounce is definitely part of the main menu I've used in the past). I generally Bounce (Mixdown), then if I'm happy and ready to split into tracks, will follow with File | Export Audio (which is quite fast if the process isn't doing all the mixing and processing, but simply splitting into tracks based on markers).
<3> Yes, you should be able to isolate the offending segment in the vocal track and apply EQ to that segment of the vocal track only. You'll want to split the offending segment into its own Object, then apply edits to that object only. Not sure what you mean by apply the change "in place"?
<3a> If you really wanted to, yes -- you could edit the vocal track independently, and then load the edited track into the project. But you need not do so. See <3>.
<3b> You could try editing after mixdown, but no need to wait until after mixdown to edit the offending segment across all tracks. I would try to <a> edit the offending segment in the vocal track only (per <3> above). See if it gets the results you desire. If you feel you need to edit the same segment in one or more other tracks, then simply split the other tracks as you've done in <3> and apply whatever EQ you need either to all the offending segments (i.e. objects) collectively, or to each one individually, customized based on the track.