Their is a lot to talk about, I'll try to add my 2c.
From the top congratulations on jumping in the deep end

. It looks like the
previous
owner (po) was spending a bit of money on the car doing it up and upgrading things.
Being a 1963 Morris 850 their is not a lot of parts left that are original, my guess is it was rebuilt at some stage using a early to mid 70's Leyland mini. It's been de-seamed and de-bumpered, the doors are from a later Delux or mini k, the seats and dash are Leyland mini items but that's all fine

.
When looking for ID numbers your mini should have a body number half way up the firewall behind the master cylinders + the one on the radiator shroud, post them up and some of the smarter people on here will be able to tell you the year and roughly the month of production. Just by looking at the engine number I'd say it's a 1098cc engine and I'd guess it has a "rod change" 4 syncro gearbox. Look under the car at the back of the gear box, if it has two rods running back to a gear stick selector it's a rod change (if it has a solid alloy box section running from the gearbox back to the gearstick it's a "remote change" gearbox).
It has "dry" rubber cone suspension, this is stiffer than the "hydro" suspension but their is no risk of it leaking and dropping the car down on it's guts, it's also much more common.
The pic you put up of the carby is actually a standard exhaust manifold not extractors, however their is already a set of extractors installed on the engine

. From the pics I can't tell if you have an inlet manifold on the engine but what you can do is get a hacksaw and cut the inlet manifold (the bit that the carby bolts to and meets up to the head) off the exhaust manifold then with a grinder or a file neaten up where you just cut so it fit's on the head without hitting the extractors.
The dizzy and cap may still be good just use a bit of fine sandpaper and rub up the connecting points (5 in the cap) and on the dizzy (the blade section of the rotor button and the top center section where it will contact the dizzy cap) also the points may need adjusting and cleaning but I don't want to go into that now. Any way all that cleaning should be done when your just about ready to try and start the engine so there's no point doing it now, just make a mental note of it.
Personally at this stage I'd only give the engine a degrease and a good pressure wash, concentrate on getting it running before you try to make it look too pretty. I wouldn't worry about the "rust" in the head it just looks normal. By the way that is where the thermostat and thermostat housing go and it is a water outlet. The flow goes from the bottom of the radiator, through the water pump, through the block and up into the head then back out the thermostat and into the top of the radiator.
Now with your parts collection;
1st pic-steering rack boots.
2nd to 4th-(I'm pretty sure) are brake slave cylinders.
5th-I'd say an outer CV (only the front has CV's) then a CV/swivel hub bearing and then another rear brake cylinder.
6th-aftermarket steering wheel boss.
7th-the rod is for the rear suspension and is part of an aftermarket "hi lo" kit sames as the alloy cone (look on say minisport's website for hi lo's and you'll gat a better idea of how they go together. The black thing is a engine mount and the blue thing is a shock but it's a fancy spax adjustable shock look them up too and you'll see why I said the po was spending a bit of money on doing the car up.
8th-Is a windscreen washer bottle and pump but I'm not 100% sure if it's from a mini, it'll still work fine though.
9th-Is the steering column. take the bolt out of the bottom and it should slip onto the spline of the steering rack which should be poking through the floor about 3/4 of an inch between the clutch and the brake pedals, you may also need to spread the spline on the bottom of the steering column by carefully tapping a flat screwdriver between the two lugs that the bolt goes through. If you can get it on great other wise look up in detail how to correctly fit a steering column and adjust the steering rack. It's easy just in depth like most things on a mini.
Getting a workshop manual from Australia will help you much more than a UK one. We branched off and started doing thins better around the start of the 60's and as time went by UK and ozzy minis kept getting even more different. Go on ebay or something and look for a manual, around $20 will get you what you need.
Good luck with it.