1) The switch is a reed switch with a droplet of mercury (the element, not the brand of outboard) in it. It's positioned such that if the engine hits an obstruction at speed and kicks way up, the droplet of mercury will short out the reed switch, which grounds the ignition and kills it. Otherwise the engine could overspeed with a lot of throttle and full load, not to mention the stress you'd get with a full-rpm engine's prop hitting the water on the way back down. So technically while you can run the engine without it, and there's a very slim chance of the engine popping up like that, it's a good idea to have all the safety systems in place that came from the factory.
The P/N is 58124A 7, "Switch Assembly" and Marineengine.com has 6 in stock. It's NLA from Mercury. $82.50, not cheap!
Here's one for around $70 on eBay: https:// www. ebay .com/itm/375030452964 You'll have to copy that link and take out the spaces, this site won't allow ebay links for some stupid reason. Their censor program will parse a complete ebay link.
Anyway, I wouldn't spend that much $$$ on one of those switches until you take it out and see if it's even gonna run right. And this switch was present on models from the 50's through late 70's and maybe beyond. If you find a 4 or 6-cyl merc in the scrapyard, it's gonna have one of these. Virtually no demand, either. So used ones aren't really worth much unless someone really needs one. I can't recall ever having a bad one, and I've worked on Hundreds of Merc over the years.
2) You should be able to order just standard throttle cables meant for Mercury outboards, they have the standard motor ends and there should be no difference at the control box end. If you have a West Marine store nearby or other type of marine outlet store, they probably have them in stock. You'll either have to go by the length printed on your existing cables, or measure-out as per the mfr's instructions of the particular brand of cable you're getting.
3) You may have to post a picture of the control box. The ignition switch, choke button, and neutral interlock microswitch are all supposed to be wired together. The choke and limit switch have wiring that solders to their particular terminal on the ignition switch. Check back to the wiring diagram I posted eariler. The tach was optional but most boxes were wired for it. The tan wire coming off one of the alternator terminals on the rectifier, is the tach signal. The white wire associated with the tach plus is switched +12V power and the black wire is ground. There's an accessory wiring harness that plugs into the tach, but those may not be so easy to find anymore and ain't gonna be cheap. You can use spade terminals and just plug them into the rubber external tach plug, to run any 12-pole modern outboard tach. They are all set up to take the pulses of the alternator and turn into a tach reading without any further calibration.
Maybe you need to post pictures of the control box end of your harness, and also the 2 control box halves, open so we can see what's in there. Then we can tell if you have all the "guts" you need to get 'er running. BTW if you're missing some pieces, they might be available on eBay and you can look up the part numbers at Marineengine.com:
www.marineengine.com/parts/mercury-outboard-parts/850-4-cyl/3493913-thru-4366801-usa
www.marineengine.com/parts/mercury-marine-accessory-parts/remote-controls-and-components/outboard-1985-and-below