I'm going to meander a bit with one possible solution with a thumbnail sketch hitting it's high points (the devil is always in the details), and to babble a bit more on other possibilities.
I have a friend who put together a pneumatic vaccum loader system, but didn't add any automation (loading simply by turning on the vacuum for 20 or 30 seconds to load, then turning it off, and waiting until it stopped dumping ... then repeating as necessary until the barrel was full). It worked fairly well, but he's since gone to oil heating (too much coal dust in his basement to use it for a laundry/rec room/computer study).
The two downsides were that the vac pump filter - he used a big Craftsman wet/dry vac for the pump - would block up with enough coal dust on a monthly basis to require replacement, and it is rather loud (sucking small rocks through aluminum piping isn't exactly quiet).
A 30mm capacitive proximity switch (NOT the more common inductive type) is used to detect fill level. They work well, and will last practically forever, but cost about $100 -$150 (see eBay comment).
My friend works in a plastics plant, and salvaged the vacuum receiver - the costliest part of the system - that he used from a decommissioned piece of obsolete equipment. A new receiver purchased from an industrial supplier places it outside economic justification. However, (and this holds for everything here) keeping an eye peeled to eBay, and waiting until reasonably priced salvage pops up (or knowing someone who can get one for nothing) keeps it in the game. There are a couple of Conair receivers up on eBay now, but, at $500 a pop, aren't what I'd consider reasonably priced for the home experimenter.
This is what a typical vacuum receiver looks like:
To add a bit of automation I'd probably use a Siemens Logo!. They aren't too costly even purchased new (~$150), and older, less capable models turn up occasionally on eBay in the $40-$60 range. The Logo model is 6ED1052-1HB00-OBAx (x could be anything from 0 - the original version to 5 (the current hardware version). Revision 3 and higher allow a bit of rudimentary HMI capability with a user programmable screen message function (and offer more 'function blocks' in the programming language).
The biggest cost here would be getting a copy of the ComfortSoft programming software, and special computer cable used to download the program you've developed into the controller. On the other hand (I'm not certain about the current generation) the original controllers could be programmed by keying directly into the front panel (a painstaking chore, however), and didn't need either.
Here is an electrical wiring sketch, and a basic program that would load for x amount of time, wait for y amount of time (to allow dumping), and trigger an alarm (and stop loading attempts) if an excessive number of load cycles were required.
I like the Logo because it gives a lot of flexibility for future additions. For instance, this particular model has an RTC (real time clock) feature, and you could do a bit of interfacing to monitor the auger motor, and add some programming to record how many minutes it has been running (that is, 'build' a run time hourmeter).
This would address the first part of your question, because, although you could add an analog form bin level sensing (the 'gas gauge' example) I'd go with elapsed run time instead.
For an auger run at constant speed x amount of coal will move in y amount of time. For instance, my coal stoker uses about 11.4 pounds of coal for every run hour, and the 55 gallon drum it feeds from holds about 230# of coal from completely full (level with the lip) to when the auger is uncovered, so I can run approximately 20 hours from complete fill to empty.
In my case, I could set up the Logo programming to give an alarm, and/or turn on a pilot light when the elapsed run time (since last reset) exceeded 18 hours, or whatever suited my fancy. However, if you automatically reloaded your hopper anyway, I don't know if I'd bother with monitoring it's level per se, and rely on the 'haven't filled in x number of cycles' alarm to let me know something was wrong.
Cheaper than the Logo! (or other controllers) would be to hard wire a set of relays for load and dump timing.
Sample hard wired timer circuit
Control relay CR1 latches up the circuit so at least one fill cycle will occur. Without this there is a good chance the vac pump would cycle on and off very quickly as coal level just uncovers the level switch - not good from a reliability or performance perspective.
TDR1 controls the load time. Once it hits setpoint the pump motor control relay turns off, and TDR2 (the dump timer) starts. When it hits setpoint CR1 falls out, and, if the level is satisfied, we're done. If not, another load cycle commences.
The motor contactor is a power relay with contacts rated for the wet/dry vacuum - a good choice here is a DIN rail mounted IEC relay. This one is a bit small for my taste, but here is one now on eBay to show they look like.
Even a home-built scratch project needs a suitable electrical enclosure - a 16x20x8 box would be my minimum. You could bolt everything to a chunk of plywood, and it would work ... but electrical stuff can burn up, and (if, say, a contactor pole burned open, and the wiring insulation caught fire) you could easily burn down the house.
Again, this type of stuff shows up on eBay, and (in addition to whatever electrical supply places are in your locale, for instance, All-Phase, Rexel, and others) there are a couple of web based stores that sell cheaply (in terms of industrial gear, that is), and sometime of this stuff can be found at web sites that sell miscellaneous surplus.
If someone has money to burn and wants to go nuts with home automation, coal burner style, check out cheaper lines of PLCs (programmable logic controllers) and HMIs (human machine interfaces).
Probably the least expensive one I'd recommend for non computer hardware gurus is the EZ-Touch PLC line.
Be aware that 'least expensive' is a relative thing, and here is in terms of typical industrial users - system costs could easily go to more than $2000 if you wanted to tie it to your home computer network, and add wild stuff like trend logging and others bells and whistles.
Siemens (Logo! controller)
Surplus (there are at least 30 other reasonable surplus resellers on the web; this is a sample)
Herbach & Rademan
Caveat - all readers should keep this in mind ... if you go this way be aware you'll spend a fair amount of time researching parts, weighing component selection decisions, and, depending on your background, learning new fabrication and programming skills.
These thoughts are batted around intended for the home hobbyist aware that they are on this road of exploration and discovery for their own education and enjoyment, and it's their responsibility to vet what they build, and be handy enough with tools in order to avoid bad consequences (burning down the house, slicing off fingers with a jigsaw, and electrocution are the first that come to mind).