Will the block reward continue halving beyond 1 satoshi if bitcoin precision goes beyond 8 decimal places? If bitcoin precision is increased beyond 8 decimals, will the block reward continue halving forever instead of eventually going from 1 satoshi to 0 satoshi?
The "8 decimals limit" is not that, but rather bitcoins are a human readable representation for 100,000,000 satoshi: The software natively computes in satoshi. 

What happens under the hood is that the limit of satoshi that a miner may claim by creating a block halves. Obviously, only whole satoshi can be claimed, (as currently they are indivisible), so after block 6,930,000 when the reward limit drops from 1.164… satoshi to 0.582… satoshi per block, one cannot claim a whole satoshi anymore, as it would be greater than the limit.

If a new smallest unit of Bitcoin would have been introduced by then, we could continue to claim parts of a satoshi until the reward limit drops below that new unit.

In fact, we will be losing out on part of a satoshi in every block starting with block 2,310,001 when the reward drops from 9,765,625 satoshi to 4,882,812.5 satoshi in approximately 2049.