Is This The Proper Way to Use Observed RVs of Different Lengths?

Questions
4

The model logp will includes two more constants from the normal, but because they are constants MCMC will essentially ignore it.

To do what you intended, you need to find a way to set up two latent variables, and let the information in the observed Y propagate back to these said latent variables, something like:

with pm.Model() as model:
    a = pm.Normal('a', 0, 10)
    b = pm.Normal('b', 0, 10, shape=2)
    
    idx = [0,0,0,0,0,1,1,1,1,1,1]
    
    ymu = pm.Normal('mu', 0, 10, shape=2)
    obs0 = pm.Normal('y0', ymu[0], 1., observed=[1, 2, 1, 2, 3])
    obs1 = pm.Normal('y1', ymu[1], 1., observed=[1, 2, 1, 2, 5, 6])
    
    y = a + b[idx] * ymu[idx]
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