Losing patience with 7 month old puppy. How do you all cope?

This is not anything to do with her being hungry, it's because she is separated from you by the stairgate and is frustrated that she can see you but not reach you. Training-wise, it is best to turn your back on her and ignore her until she is quiet. If this is difficult when you are going to answer the phone, it would be best to throw down a handful of kibble in the kitchen before you go answer it, so she is then busy sniffing out the kibble instead of focussing on where you are and barking.

Well, that's a food motivation emergency. Do you want to be mixing her food with chicken or cheese all her life to get her to eat it? Is she training you, or are you training her??

Put down the food YOU want to feed. If she walks away from it, IMMEDIATELY remove it and offer no more food until the next meal time. Please resist thoughts like 'she must be hungry'. She is not going to die from missing a meal or two, or even several days... Once you have her devouring her food the second it goes down, then you will need to move to training her with it - so she doesn't get it for free and has to work for it.

It is very important to establish excellent food motivation from a young age, if you want to be able to train a dog effectively and around high distractions.