Answer to question 1: There are two circuits being executed because you are trying to find the expectation value of the Hamiltonian, $\langle \psi |H|\psi\rangle$ = $\langle \psi | \sum_i \alpha_i P_i | \psi \rangle = \sum_i \alpha_i \langle \psi|P_i|\psi\rangle $. So naively each circuit is representing one of the calculation of $\langle \psi|P_i|\psi\rangle $. For example, the electronic Hamiltonian for $H_2$ at bond distance 1.5 Angstrom under Parity Mapping with two-qubit reduction can be written as:
$$H = -1.009II + 0.1291IZ + -0.1291ZI -0.0041ZZ + 0.2295XX $$
but since $II, IZ, ZI, ZZ$ are in the same tensor product basis, they can be evaluated as single quantum circuit, and you just need to do some post processing calculations... that is you don't have to run 4 different quantum circuits, one for each. But $\langle XX \rangle$ need to have its own circuit. Hence the reason why you see two circuits here.
Regarding to question 2: I don't see how you do the transpilation process so I can't say much. When I see your orginial circuit:
and look at ibmq_16_device which has qubit layout as
I would map $q_0 \to 1, q_5 \to 2, q_1 \to 3, q_2 \to 4, q_3 \to 5, q_4 \to 6 $ then this way your circuit can be executed in just depth of 2. There are other mapping you could do, of course. When I run the original circuit with optimization_level = 3 in Qiskit, I have the following transpiled circuit:
UPDATE AFTER COMMENT BY OP ON CREATING HIS/HER OWN ANSATZE FOR VQE EVALUATIONS:
Regarding to OP comment on create a parametrized Ansatze for his work on VQE. An Ansatze is just a a parametrized quantum circuit, and you can create parametetrized quantum circuit pretty easy. Here is an example of how to do that with the circuit you have in mind:
%matplotlib inline
# Importing standard Qiskit libraries
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit import QuantumCircuit, ParameterVector
from qiskit.compiler import transpile, assemble
from qiskit.visualization import *
provider = IBMQ.load_account()
var_form = QuantumCircuit(6)
params = ParameterVector('a', 6)
for i in range(6):
var_form.ry(params[i],i)
var_form.cx(1,2)
var_form.cx(3,4)
var_form.cx(0,5)
This will give you the following parametrized circuit:
You can now pass this into your VQE function! Hope this helps. :)
Also note that Qiskit does offer a few Heuristic Ansatze, like EfficientSU2 or ExcitationPreserving, TwoLocal, etc...
