1. "will both DDR3 and DDR4 RAM work"?
No. You may ONLY install what the motherboard supports (unless you like having a dead board?)

2. 8GB is enough for most uses. You didn't share why you want to change. So I'm going to think it's for speed or such. Let's share the OTHER thing that makes a lot of PCs slow. The HDD (Hard Disk Drive.) For under 99USD I can find on sale 1TB SSDs. 500GB SSDs are even cheaper and are fine for most users. Before you upgrade the RAM, be sure to remove the HDD in favor of SSD.