Both are valid addresses and can be assigned to hosts.
Network address is only really used for directly attached networks, non directly attached networks will route to any address in the block correctly.
Same for broadcast address, they're also relative to whatever block you're talking about at the time, so whilst 3.255.255.255 is the broadcast for 3.0.0.0/8 subnet it's just another "usable" address in the 3.0.0.0/5 subnet and when you send a packet then you, and probably your router, don't know what subnets in use on the other side :) (unless it's directly attached)
There's no reason why you can't assign 3.0.0.0 to a host, it'll work fine. Just make sure you don't put anything else there by convention.
3.255.255.255 would be the default broadcast address, but not only can you use a different address (in fact, any address you want for broadcast, you just need to configure it), but this is also not a real /8... it's 3.0.0.0/15 according to ARIN.
They delegated 3.0.0.0/15 to Singapore, out of the AWS 3.0.0.0/9 block, which is adjacent to their 3.128.0.0/9 block... which gives them all of 3.0.0.0/8...
Broadcast addresses have no meaning outside of a broadcast domain / subnet. Nobody would use a full /9 as a subnet. It would be split into much smaller blocks...
