That being said, by the time the last Bitcoin is mined—roughly 115 years from now—the cost of mining will likely have dropped significantly due to major advancements in computing and electricity generation.
The cost of mining is primarily determined by the value of the block reward (i.e. subsidy plus fees) because of the difficulty adjustment and the economics of mining. It is not related to technology or energy prices.
And after 1 bit becomes 0 is the network programmed to stop 'dividing/cutting' it or will it forever divide 0 by 2 (only to get 0 again) every 210 000 blocks?
That's an odd question. First, the network isn't programmed, each node in the network is programmed. Second, whether a node's software divides 0 by 2 to get 0 or it just says 0 is irrelevant because both agree that the amount is 0.