if they can ping by IP but not by name, then the issue is DNS, not firewall. If the DNS translation request cannot get past the firewall, then it will fail. The fact that pinging by IP works shows that the ACL and NAT are setup correctly for ping at least. Now you just need to identify if the same areas are configured for dns resolution
RE: 192.168,3.5 can not communicate with anything on 192.168.1.x
This sounds like a netmask problem too. 255.255.252.0 yes? Your network actually has a bunch more IP's than you intended, I guess
Address: 192.168.1.0
Netmask: 255.255.252.0 = 22
Wildcard: 0.0.3.255
=>
Network: 192.168.0.0/22
Broadcast: 192.168.3.255
HostMin: 192.168.0.1
HostMax: 192.168.3.254
Hosts/Net: 1022
Does everything have the correct netmask and gateway information? Can you post an IPconfig /all from a .3 workstation AND post the ASA's config please?