Yes, the exact date of the next Bitcoin halving can be accurately determined in advance. The Bitcoin protocol initiates a halving event on the Bitcoin blockchain when the number of blocks on the chain reaches 210,000 (approximately every four years).
Nope, exact halving date can't be known in advance, the best we can to is estimate it and all the websites with halving counters do exactly that. All that we know is that the next halving will happen at the block 840,000 but problem is that we can't be 100% sure when that will happen because blocks are not mined at the exactly 10 minutes interval and instead that's just an approximate average.