Training Error decreasing with each epoch
I am not very sure about your case, usually I have seen the same problem but in the other direction, you can take a look here:

Quora loss drecrease, accuaracy constant
Cross validated loss drecrease, accuaracy constant

I would guess that your DNN is getting more answers right but without impoving its confidence  a lot.
Regarding your other questions, I would advise you to start with simplest possible model, for example, in this case it would be using the vgg16 (which is widely more used than the vgg19) and the default parameters ( number of neurons, optimization function...) Once you have something working you can start tuning and modifying things.