[Python] KLM protocol - NS_{-1} gate in strawberryfields

I'm new to strawberryfields and I'm trying to implement the gate in Fig. 1 of KLM's 2001 paper.

This is my code:

import numpy as np
import strawberryfields as sf
from strawberryfields import ops
from thewalrus.quantum import state_vector

prog = sf.Program(3)

phi_1 = prog.params('phi_1')
theta_1 = prog.params('theta_1')
phi_2 = prog.params('phi_2')
theta_2 = prog.params('theta_2')
phi_3 = prog.params('phi_3')
theta_3 = prog.params('theta_3')
phi_4 = prog.params('phi_4')

with prog.context as q:
ops.Fock(2) | q[0]
ops.Fock(1) | q[1]
ops.Fock(0) | q[2]

ops.Pgate(phi_4) | q[0]
ops.BSgate(theta_1,phi_1) | (q[1], q[2])
ops.BSgate(theta_2,phi_2) | (q[0], q[1])
ops.BSgate(theta_3,phi_3) | (q[1], q[2])

ops.MeasureFock(select=1) | q[1]
ops.MeasureFock(select=0) | q[2]


eng = sf.Engine("fock", backend_options={"cutoff_dim": 10})

result = eng.run(prog,modes=[0],args={
'theta_1': 22.5 * np.pi/180.0,
'theta_2': 65.5302 * np.pi/180.0,
'theta_3': -22.5 * np.pi/180.0,
'phi_1': 0.0,
'phi_2': 0.0,
'phi_3': 0.0,
'phi_4': 180.0 * np.pi/180.0,
})

state = result.state
print(state)
print(state.data)
print(result.samples)


I have a few questions:

1. 
   How can I start mode 0 on a superposition of Fock states? (i.e., alpha_0 |0> + alpha_1 |1> + alpha_2 |2>)
   
   
2. 
   How can I then get the success probability? (i.e., the heralding pattern I specify with select in MeasureFock).
   
   
3. 
   How can I then verify I get a minus sign in front of |2>?
   

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