Hi CarinaBob, welcome to Outdoorking. Unless your name is a remarkable coincidence, it sounds as if you have or used to have a model of car that I think was never officially imported into Australia.
First, you might find the Instruction Manual for the larger versions of your mower useful. (I think nearly all of it applies to your mower.) You can download it free from here:
http://www.oldlawnmowerclub.co.uk/sites/default/files/opmanual/Atco%20172055.pdf1. Kickstart Spring.
Spares for ATCO mowers may be a bit difficult in Australia - they exist, but it may not be easy to find the people who have them. If your request on Outdoorking does not bear fruit, I suggest you contact the UK Old Lawnmower Club - it is a good source of information on old British mowers such as yours. There are spare parts places in Britain who will have what you need, but their prices seem rather frightening to me. This is especially true of simple things like the kickstart spring, which can be made in a very short time from the right diameter spring steel wire.
2. Clutch Adjustment
The procedure for adjusting the clutch is on Page 6 of the Instruction Manual. I suggest you follow it closely. Remember, check that the clutch lever has free movement and adjust the linkage if necessary, as described. Do not adjust the clutch itself unless it slips even when the linkage has been correctly adjusted.
3. Re-Sharpening
No, sharpening the reel or bedknife is not a job that can be done at home. I can recall the days when people who had a lathe sometimes did a reel-sharpening job themselves, but results were rather ordinary compared with even a fairly poor professional job, and grinding the bedknife at home is far more difficult than the reel. I suggest you contact a local greenkeeper at a bowls club and ask who sharpens their reels and bedknives. You will need to consider the condition of the reel bearings at the same time: it is not practical to maintain the reel in good cutting condition unless the reel bearings are new or indistinguishable from new.
