Greetings,
For emergency descent, please refere to Jepessen part C, emergency and just apply the laid down procedure as per the area you are flying within, Europe for example says turn away from the traffic, talk to ATC (if you can) and then descent (O21 mask and crew com always applies first)
Your intructor did it the Boeing way "keep heading"
After RTO, you set the park brake on, PA "cabin crew at station" and deal with the emergency and ground evac if required.
Now if no ground evac is NOT required, then look at the brake temp, to be sure that it safe to resume taxy,AND be able to stop again.
remember that brakes transform cynetic energy into heat energy using friction, and have a heat absorbtion capacity that IS NOT unlimited.
The worst that can happen is that the fuse will melt and the tyres will deflate, remembering that your number one priority is passenger/crew safety, brake can burn, be glowing tyre can burst, your priority is ....
Engine fire, RTO and wind from the .... this emergency is time critical, but there is always a smart A##S who wants to outsmart and impress by saying that the wind is from the ... I will then turn ... I must admit though that in a movie, it will have some effect, in real life, different ball game, cross wind meaning you will turn at 90 deg from the runway, or run the risk of have a part of the aircraft outside the runway (which doesnot have the strenght to sustain the aircraft weight....
As far as I am concern, I include the wind information to the CSD, during the NITES briefing, and deal with the priority.
I never heard of RA CLIMB, baring in mind that RA only trigger reflexive maneuvers, ATC are familiar with TCAS, whereas RA

I doubt it, on top on that RA will sound different, depending on who is saying it