Is the block reward for Namecoin halving scheduled the same way as Bitcoin, or is there a different schedule?
Yes, it's 50, as documented here: http://www.bluishcoder.co.nz/2011/05/12/namecoin-a-dns-alternative-based-on-bitcoin.html
The reward for solving a block will halve every 210,000 blocks (around 4 yrs), like Bitcoins.
When namecoins are spent to register a domain name, they are destroyed. More details here: https://github.com/vinced/namecoin/blob/master/FAQ.md
Note that even though the mining reward remains constant, the network fee to register a domain goes down quickly over time. Quote: "The network fee is initially high, but will be negligible after a couple of years. It is used to slow down the initial registration rate so that plenty of desirable names are left for late adopters."