Question on B737CL TO performance
 

Assuming there are no RTOW tables, OPT software, etc, only FCOM, QRH and FPPM to determine takeoff performance.

Having determined performance-limited max TO weight (Field Limit, Obstacle, Climb, Tire, Brake Energy), I arrived at a certain figure, let's assume it's controlled by Field Limit. I then find assumed temperature using "performance in flight" tables from FCOM, N1 for it and corresponding V1-Vr-V2. Now, is this assumed temperature also have to be re-checked against all those performance-limited weights (in lieu of OAT, especially with Field Limit graph), or is 25% maximum assumed thrust reduction already somehow incorporated into Limit graphs? (FCOM just says to find V speeds for assumed temp in lieu of OAT).

My second question, are Obstacle Limit graphs from FPPM (or tables from FCOM) cover performance for engine-out condition?

Finally, could someone please share obstacle/gradient graphs for takeoff segments from AFM (B737-300, 20K engines), please PM me. This is for self-research/study, not actual operations.

Thank you!

No, the figures need not be rechecked, the assumed temperature found is reducing engine output to a safe extent.
Obstacle limits are not for engine out scenario, only two engined case.