Constant Voltage model pf Diode circuit analysis
If the same circuit in ideal model had both \$D_1\$, \$D_2\$ conducting, does that mean in constant voltage model \$D_1\$ and \$D_2\$ will conduct?


Need not be.

I see a few mistakes in the solution you have given here:


In the KVL, you missed one DC source. There are two voltage sources (+5V and -5V) in the loop.
The value of \$I_1\$ will be in milli-amps (0 ~ 1mA).  
Voltage at node B is not \$5k \times I_1\$. It is \$5 - 5k \times I_1\$