I am not sure about the omnigun question - never tried to switch to a gadgeteer later in the game - but I do remember hearing that you get one. You could always get one off of Madras though.
As for ex-bards and music. Yes, they can keep playing instruments after they leave the bard class. To play instruements, there are 2 requirements. One, a minimum score in the music skill; two a minimum bard level has to have been attained. The highest level required to play the best bard instruments is 18. So if you are an 18th level bard and have 100 (and maybe just a 90, can't remember what the highest music skill requirement was) music, you could switch to another class and still be able to play all bard instruments.
At any rate, switching to a gadgy later in the game isn't such a good idea - the omnigun is weak until very high levels, and you'll need a high engineering skill to use the better gadgets. Good classes to multi to from Bard are Rogue or Fighter, to pick up their attack modes (backstab/beserk). But you'll lose the ability to wear all the cool stat-enhancing bard items. I'd say unless you planned the multiclass out carefully/early on, don't bother with it now.
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