What is the actual sequence of events for the descent ? Not sure if you still have DME but I assume your computer tells you at what point you need to start and you complete check list before that point.
The descent will require around 3.5 miles per thousand feet of altitude. So, roughly 130 miles from FL370. That's track miles of course, and not just the DME distance, so if you have to fly past the airfield and then come in from the other side, that would mean you'd wait until around 100 miles from the destination.
Do you still request ATC approval to descend at a given point or do they tell you ?
Normally you ask ATC for a clearance around 8 miles before you get to the descent point...that gives time for an answer, and for any others to make some room on the radio. In many places ATC will preempt with either an early descent (because they want you out of your level NOW), or a clearance to descend 'when ready', in which case you just need to tell them when you actually leave the level. Often too, ATC will issue a clearance to descend, but with a requirement to be at a certain height by a given spot...that is normally lower than the optimum profile and has the effect of causing an earlier descent.
Virtually all approaches are planned via a STAR (standard instrument arrival). These are a series of laid down tracks which take aircraft to the start points for the actual approach. Many include height restrictions. The FMCs will be programmed with the actual approach (often not all of it, we put in what we expect to do from experience) and the STAR, which will be joined logically to the flight planned track. In some places you normally fly the plan all the way, whilst in others it's little more than something to keep the FMC busy, as you never fly any part of it, either being radar vectored, or cleared directly to points.
You never really know what ATC are up to, so there's a lot of bet hedging going on. If they hold you at an altitude that tends to put you above the planned, many people slow up immediately, and will then accelerate when cleared lower. I'm sure that drives ATC nuts, but it's a attempt at energy management without having to use the speed brakes, immediately after a power application. Speed changes sometimes come at what seem to be random intervals, and often a speed up request comes immediately after a requirement to slow down (Oz is the worst offender for that).
On final ATC trick is that of 'cutting you in'. On some arrivals, it's quite simple to cut quite some distance out of the approach (for instance arriving from Melbourne onto Sydney 16 or 34). You need to keep a very wary eye on just where the base turn point is, relative you your plan, as turning early can suddenly move you from being on profile, to 3 or 4 thousand feet high. Correcting that distance inside 20 miles to run is very different to doing so 100 miles out.
The flight management systems themselves vary enormously in their behaviour..as do the aircraft. In a Boeing, selecting heading during the descent will not affect the vertical mode (VNAV), whilst doing the same in an Airbus immediately removes vertical navigation as well. The systems themselves sometimes just simply lose the plot vertically (the 380 is the worst I've seen at this), and either tell you lies, or sulk and say nothing. Keeping a mental picture of just where you are is still very necessary.
Navigationally, DME is still used, but it isn't as accurate as the FMC derived position from the combined IRS and GPS....as long as it's not sulking too.
At what altitude increments do you need to contact ATC before continuing the descent ?
ATC will clear you to a level below where you are. It could be a 1000 feet, or 20,000 feet, and it will vary from day to day (though in some cases the clearances are very standardised). Normally around 500 feet before we get there we call "approaching", which is just our attempt to remind them that we'd like to avoid levelling off.
What latitude do you have to alter course during the descent ? For instance you may not want to fly through a coughpy cloud.
None normally (in controlled airspace). If there is weather you get a clearance to avoid it as required.
Why do heavy / wide body acft seem to take a lot longer approach path on finals than 737 size acft.
A number of reasons. One is simply that the pilots of the smaller aircraft tend to get a lot more practice. Secondly is that the larger aircraft are almost always ending long flights, and the pilots will be tired, and that is never a good time to show how smart you are (or aren't). A look at the 34 arrivals into Melbourne shows one particular approach from over Essendon which gives very little 'finals'..so the big jets can certainly do it if needed. The longer the finals the more chance you have of fixing any errors in either line up or energy. A look on youtube at some of the films from Kai Tak shows how things can go very wrong with short final approaches.
And at the end of the day..it's a lot easier to park a Barina than it is a Mack.