I just had a play-around with some numbers. Suppose the underlying price today is at point (A), which happens to be 100. Suppose point (B) is 108. We're talking 1-year expiry, with rates zero and implied volatility = 25% for all strikes.
For the call-spread: Suppose you bought ATM call at strike $K1=100$ and sold OTM call at strike $K2=108$. Your net cashflow is negative, because the ATM call is more expensive than the OTM call (=> so this is a "credit call spread", not a "debit call spread".)
Suppose that the price of the ATM call is 8.4 units, and the price of the OTM call is 5.3 units. Your net cash outflow is -3.1 units. Your pay-off diagram at maturity will be: (i) -3.1 units between underlying price being zero and underlying price being $K1=100$, then linearly to zero until underlying price being $103.1$, then linearly positive until underlying price $108$, at which the pay-off becomes constant positive +4.9 until underlying price infinity:

For the put spread: Suppose you bought ATM put at strike $K1=100$ and sold ITM put at strike $K2=108$. Your net cashflow is positive, because the ITM put is more expensive that the ATM put (=> so this is a "debit put spread", not a "credit put spread".)
Suppose that the price of the ATM put is 8.4 units, and the price of the ITM put is 13.1 units. Your net cash outflow is +4.7 units. Your pay-off diagram at maturity will be: (i) +4.7 units between underlying price being infinity and underlying price being $108$, then linearly to zero until underlying price $103.3$, then linearly negative until underlying price $100$, at which the pay-off becomes constant negative -3.3 until underlying price zero:

Whilst both spreads look very similar, effectively, the credit call spread has a lower downside and a higher upside: that's why it should be "more expensive" than the debit put spread: but the numbers look way out of proportion. I actually used Black-Scholes pricer, rather than guessing the option prices: but obviously in real life, the Imp Vols would most definitely be different on the different strikes, and would cause the structure to be more proportionally priced.
When I have more time, I'll try to edit the answer to include a structure with a symmetrical pay-off at maturity.
I know this hasn't addressed the points you specifically asked for, but at least it's a start.