Will transaction confirmation time be reduced as the network size increases? Right now it takes 6 confirmations, which takes about an hour to verify a transaction. Will the rate at which transactions confirm become faster over time?
No. The average time per confirmation will always be about 10 minutes (but it's possible that the variance will be lower in the future). And the number of confirmations required to prevent double-spending by an agent with a given hashrate will also not change (6 is an arbitrary number reflecting a "low enough" probability for someone with a "high enough" hashrate).

What will change is services to bridge the gap. There will be split-key eWallets which cannot steal your money on one hand, and can have trusted green addresses on the other; and there will be insurance agents such as https://zipconf.com/ that absorb confirmation risk based on their model of the probabilities of double-spending.