Half bridge DC-DC converter circuit analysis
Your flyback analysis appears to be correct.

For the half-bridge type shown you can assume that the mid-point of C1 and C2 is Vin/2 (and DC) for analysis. Therefore I would put: -

For M1 is conducting: VIN -> M1 -> T1-> VIN/2


  Also, any direction to the current and mosfet drain voltage
  characteristics (plots) will be appreciated.


Current flows into the left side of T1 when M1 activates and flows out from that point when M2 activates. Without a part number for the MOSFET the 2nd part cannot be answered.