Do second-hand purchases count towards expenditure?

Can I purchase 2nd hand equipment as an asset for my business and then add that full amount to my business costs? The item will come in under R7000, so I believe I can write the depreciation off within one tax year.

Yes, that is correct - low value assets less than R7,000 can be written-off in full in the year of purchase. This will also apply to to the purchase price you paid for the second hand goods.