Question

Opamp question - Is the branch that goes to ground in parallel with the branch that goes to Vout?

Answer 1

Here's the opamp

Answer 2

Not entirely. What is important for opamp circuits to remeber is that \[i_+ = i_- = 0\] and that \[v_+ = v_-\]
If you start from those two conditions, you'll find that only a part of the branches are parallel.