When you increase throttle and engine rpms what happens?

Really depends who you think your audience is. Lay people may just want to know how a plane flys or why certain things happen on commercial flights. Pilots may want to learn about skills/ratings they havent acquired yet, recent incidents.

160 is the final approach heading to runway 18. You notice that this approach does not align exactly with the runway, you make a slight right turn to land. 115deg is the outbound leg heading for a procedure turn and 295 is the return heading from the procedure turn, from which you would turn 160 on final and fly the 160 line to the missed approach point. DME is required for this approach so you would either need DME or a GPS that can supply distance information. To fly this full approach (from southerly directions) you would fly to the VOR, fly outbound at 3000' MSL on a 340 heading for about 7 miles then turn left to heading 115 for 1 minute then right turn to 295 and intercept the 340 radial, turn right to 160 and descend to 2300' by GRAMA and continue descending to 1220" at 1.6 DME from the VOR. From that point, if you have the proper visual cues you may descend below 1220' to land, if you can't see the runway environment from 1220 feet at 1.6 DME then you must stay at that altitude until you do see it or you reach the missed approach point at .3DME. There's a very real reason that an instrument rating is required for IFR flight. It takes a lot of training and practice to learn to do it right - and even then you may not have it all correct. (I may well have missed something on this approach but I haven't been IFR current in several years)

Usually it is airspeed of the aircraft. Each aircraft has different airspeed requirements for operation the flaps or landing gear. Usually that speed is determined by the airframe manufacturers and the design of the flap system component. You could built it strong enough to handle any airspeed, but a plane can only carry so much weight. If you built everything to work without any limitations you might have an airplane too heavy to fly. Designing a plane is a balance between lifting capability and weight. Both of these are important design parameters.

Your question is a good one - but the answer is much more complicated that you would expect. Think about driving your car from point A to point B across a city. Lots of paths - some shorter than others, but the shortest path may not be the quickest. Or the quickest may involve a toll road - and you may or may not be in a hurry.

The usual most important factor (for commercial operations, at least) is to save money, while still arriving on time. Airplanes in the air are subject to the winds aloft, which will generally be at different strengths AND DIRECTIONS at different altitudes. Most airplanes operate more efficiently at higher altitudes (up to limits), but at those higher altitudes the plane may face stiffer headwind. Further, it costs time and fuel to climb to those altitudes, and you will not regain coming down as much as it took going up. [Think of a bicycle on hilly terrain vs. level ground.]

So what's the answer? Well, for most trips the pilot will consider all these factors. They are taught during training how to plan the flight in terms of time and fuel required, and to include in that especially the winds at different altitudes. Then they will pick the altitude, whatever that is, that maximizes the results that they consider most important.

The DC10 was an excellent aircraft, with a long and successful service history. They are still flying in many countries, and in the US you see lots of them with the freight haulers.
There were, unfortunately, a few (very few) high profile crashes - which is probably what you refer to. The infamous "engine drop" issue was bad maintenance - not a problem with the aircraft design. And the Sioux City crash (pilot Al Haynes) was caused by a truly unlikely event that simply proves that even low odds can happen. [An uncontained blade failure on the #2 engine ejected "just right" (or just wrong) and cut the one small spot where all the control surface hydraulic lines came briefly together.]
The reason that DC10's are no longer in primary service is attributable to two things:
1. Older fuel hungry engines (3 of them), compared to the more fuel efficient twin engine design. And the changes to ETOPS regulations that now allow twin engine airliners to fly trans-ocean.
2. Certification of the aircraft with a three-person crew, in stead of the cheaper two-person flight crew common now. [The freight haulers get around this by cross training the loadmaster (only needed on the ground) to also be the flight engineer (only needed in the air).

Departure controllers have blocks of airspace with altitude limits. Chances are that there was other traffic that they needed to have out of the way so they held him at 5000 before clearing him to the next controller's airspace.

I suspect that the idea of max climb plus glide is not a new one, and that, if it really were cost-effective on fuel, we would know about it.