Not sure about the separation anxiety, but I make Gina wait and let me walk through a door before she does, or into another room. I would suggest some training classes, and socialization at a dog park, or just around your neighborhood. Good Luck, and I know others here can give advise on the separation issues. Welcome to YT.
Cheers Quad & Gina
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RIP Megan 3/1998-5/28/2013