Lots of issues here...
All goods traffic, except "special traffic" (there always have to be exceptions) was moved on scheduled trains. A large and busy station might have several trains in and out in the day. The most minor stations might have only one goods train a week. In between there were (naturally) numerous variations. From the modeller's view point the more likely and preferable pattern would probably be a goods train to deliver and collect in the morning and another in the afternoon - probably timed fairly well apart. This provides activity. However, there would always be a minimum of shunting - two reasons - train crew don't want to mess about and there is a practical need to not waste time - oh - and third - you can't load/unload a wagon wile it is being messed about with - and - other side - there are limitations on shunting a wagon if it is the process of being loaded/unloaded - the load will tend to not be secured.
If there is a large enough yard the am and pm might be doubled up by having a pair for each direction of travel - mainly on a through line. On dead-ends the ingoing train will drop off while the outgoing train will collect - as a broad guide line. There might be a small amount of very local traffic.
Broadly speaking goods vans were not used for "groupage" - known as "LCL" - "less than car load" in the USA. Anything a lot less than a van or wagon load would tend to travel under the heading "smalls" - which could go by passenger train (1 ton "evenly distributed" in an available brake van/luggage van) - or by a "parcels" train. In many ways the railways provided service that achieved pretty much what modern courier road services provide - including the need to wait at home all day not knowing when the delivery would/might show up. There were various means of getting parcels of all sorts of sizes from stations to addresses (of all kinds - from homes to large factories). The railways provided service!
There were increasingly vast systems of wagon movement planning. As far as practical empty running was avoided. Once unloaded at a station a wagon might sit there (so long as it wasn't in the way) or it might be returned to a pre-planned location until it had its next job lined up. As an example - wagons from dead end branch lines might return to the junction - provided there was room for them. On the other hand, when the junction was full (or going to be) empties could be shuffled off down a branch line to get them out of the way. How far they went down the branch would depend on local and current conditions. (Sometimes seasonal traffic would create large collections of "pre-positioned" stock - not always at obvious places). This shuffling could apply to loaded wagons as well as empties at times, with certain types of traffic - subject to the loads not tending to be pilfered.
One interesting option for modellers is as follows...
Where traffic needed to be got out of the way from a large station and forwarded a train could be booked to leave "rough marshalled" at a specific time / in a defined pathway. Somewhere on the route it would then be booked into appropriate sidings/yard (i.e. large enough and clear enough) for the various wagons to be re-marshalled into groups for common destinations. Now this option does provide excuse for all sorts of playing trains!
In the next OP section I suspect there are two parts. First - a non-specific wagon of any kind would be worked away from a station with a load as far as possible - so long as it didn't have to wait long for it. Next option would be for a short trip to where a load was ready/waiting (or would be very soon).
Then we get to specific wagons. Tank wagons in particular tended to return empty - and would often be in specific point-to-point traffic - even when only running as individuals. due to coal being dusty/mucky the same could apply to anything carrying coal and coal products - with specific attachments to collieries, Private Owners or both.
What are the "widgets"? Can they be packed in any van or do they need clean vans, "Shocvans", ventilated vans...? Or any other specific requirements? Securing the widget load might mean that it would be more effective to keep using the same van/set of vans rather than messing about keep securing the load - this might mean a saving on wood packing - which could be repeatedly used - or it could mean special fittings. Any van with special fittings would usually be marked for the specific traffic. Anything on a regular job tended to be marked for it - or at least "return to..."
2nd part of 2nd section. Not entirely sure of the meaning... rail vans could not be towed around by a tractor "off track" - not because they couldn't be towed - but because their steel, flanged wheels would wreck any surface - and they would probably bog down.
That said - shunting (on rail) could be done by tractors in various ways. Prior to tractors it could be done with horses - plus, with suitable gradients, it could be done by manpower - sometimes using pinch bars. In larger yards there was also capstan shunting.
I don't know if the OP is aware that wagon turntables remained in use at least to the end of the railways being "Common Carriers" - sometime ???
I don't recall when. Some factories still have traces of their tracks and wagon turntables.
Factories... Tended to be built up close to the railway if/when they would need a lot of rail service. Track could leave the rail companies boundary - either maintained and/or worked by the rail company or privately depending on what was contracted between the parties. Depending on the arrangement(s) the rail company might let their locos into the factory tracks or not. Usually factory locos were not allowed out onto rail company tracks. Naturally other means of locomotion operated as appropriate/as arranged.
Where there weren't factory sidings transhipment would be required. This could be to railway owned/provided (at a price) road vehicles, the factory's vehicles or other contractors vehicles. Another alternative for suitable loads was transhipment to a narrow gauge rail system. These were used for all sort of traffic - sometimes over quite long distances. Minerals, timber, hospital, military supplies among many other things were moved by narrow gauge from local stations. These narrow gauge tracks did not usually (if ever?) run on public roads or unfenced next to them. They tended to cross fields on very limited formations. A few were more substantial - a whole subject in itself. These lines varied in life span, equipment - and a whole lot of things. Before the convenience of internal combustion really got hold they could even be used in the construction of housing estates.
Stock was not usually put into a goods shed except to unload/load it there or when the load needed to be kept secure (from pilfering) Goods shed accommodation wasn't often large and space was at a premium.
Stock cost money so it would be kept earning money as much as possible. This meant finding a balance between holding it back for a load and sending it to where a load was. "Standage" was chargeable. Using a rail vehicle as a warehouse cost the load owner or shipper money - although it could be arranged - especially for bulk coal.