Are there any hacks or types of shifters that let you quickly shift down across the gear range? On my 10 speed to get down to gear 1, I have to pump the shifter 5 times. Is there an easy way to shift down without multiple pumps?
To answer this part of the question:
Are there any hacks or types of shifters that let you quickly shift down across the gear range
Grip shifters should allow one to click through the whole range of gears in one rotation (provided that one's wrist can manage to make such a movement). The same applies to certain bar-end and downtube shifters (with no "return to neutral" function).
Whether or not a conventional rear derailleur will be able to survive such a drastic change of its cage offset is another question. I would expect that in a worst case it is possible to skew the chain so much that it will jam and break, or hopp off the cassette. You can imitate this when a bike is in a stand with its chain in one of the extreme positions on the cassette. Operate the rear shifter to switch to another extreme position (e.g. from 1 to 10, or from 10 to 1) without spinning the cranks. Then try to spin up the cranks as fast as possible and observe the chain to jump or to screech.
Having an internal gear hub (or a frame-mounted gearbox), however, should in general allow to make such rapid switches as the chain does not change its position. There may be other limitations, like a requirement to stop pedaling for a short moment to allow the gears to settle in new positions, but it still possible to go from the first to the 18-th gear and back in one go, even when the bike is completely still.
Most Shimano flat bar shifters have RAPIDFIRE PLUS which allows down shift of 3 gears with one push. It is quite a long stroke to shift three gears, so often its just as quick, and easier to activate the shiftier twice.
To down shift the full range of gears in one or two actions would not be a normally be needed. The time (Which corresponds to distance as it takes wheel revolutions for the chain to get picked up on the ramps and moved up the cluster) for the chain to move across the cassette and get picked up on the sprockets is usually the limiting factor in such gear changes.
If you are finding yourself having to move the chain more than a couple of gears in a single action, its likely your gear selection and timing of gear changes needs work.
There is one way that's easy but very expensive: install electronic shifting. On Shimano road systems, you can hold down the shifter and it will shift through the entire range. I'm not familiar with the MTB or Urban (Alfine) versions, but I'd expect that they can do similar.
The question's wording makes me think that when you say shift down, you mean shift to smaller cogs. (Whatever direction you mean, electronic shifting can do it.) Another expensive alternative is switching to drop bars and Campagnolo mechanical shifters. Current generation Chorus, Record, or Super Record shifters can go down as many as 5 cogs with one push of the thumb button (note that they are 12-speed, so you're talking 3 sweeps of the thumb button). If you must be able to do it in one push, then I think that the 10-speed shifters (any level) can do this.
Neither of these solutions is likely to be worth it for you. As others have alluded to, almost every other rider has had to learn to manage with shifting in advance of the terrain changing. It's just one of those cognitive skills that we pick up over time.
On most shifters, it's possible to shift 2 or 3 gears at a time. But 10 in one shift is not likely possible. Shimano's Rapidfire Plus shifters help. Most drop bar shifters can shift 2 gears in one motion. But as noted its actually quite dangerous to rapidly shift more than 2 or 3 gears at a time.
Chain tension - the rear derailleur can't handle rapidly shifting. It tends to go slack and the chain skips along the cogs. This has happened to me once or twice. When it starts to slip, you can correct this by shifting back up to 'catch' the chain on the cog. Clutched rear deraileurs tend to perform better in this situation.
Chain strain - the chain doesn't take lateral loads well. Large rapid shift can put too much lateral strain on the chain and cause it to break.
As an alternative to large shifts along your rear cassette, you could try a compact crankset so that you can easily jump between 34- and 50-tooth chainrings. This is equivalent to about 3 or 4 cogs in the rear, depending on your rear cassette and where you are in it.