When two particles with mass m collide head-on, are the followings true?

1. $p_{total}^{2}=\frac{\left( E_{1}+E_{2} \right)^{2}}{c^{2}} = (2m)^{2}c^{2}$ (If so, that means $E_{1}$ and $E_{2}$ vary between reference frames, but the $p_{total}^{2}=4m^{2}c^{2}$ always hold. )

2. The $p_{total}^{2}$ is conserved in interactions. (I think $m^{2}c^{2}$ is not conserved in interactions. Am I correct?)

When a particle with mass m collides with a fixed target with the same mass, are the followings true?

1. $p_{total}^{2}=\frac{\left( E_{1}+E_{2} \right)^{2}}{c^{2}} = (2m)^{2}c^{2}$ (If so, that means $E_{1}$ and $E_{2}$ vary between reference frames, but the $p_{total}^{2}=4m^{2}c^{2}$ always hold. )

2. The $p_{total}^{2}$ is conserved after the collision. (Is the $p_{total}^{2}$ not only invariant, but also conserved?)