I have heard of some termite 'systems' in which a pest control company inserts a spike into the ground around the house to detect and kill termites.
QUESTION: To save costs, can the same (or similar) system be purchased and operated by the homeowner without going thru a pest control company?

Those systems (at least hte ones I've seen) are not for termite control, merely detection so the termite companies know its time to come spray again... The best way to keep termites at bay is to keep all wood and cellulose containing debris (including paper, leaves, woodpiles, etc.) away from the house and to prevent direct wood to ground contact between the house and the ground.