Can I put Virtual Server in different subnet from Self-IP?

Of course you can. You need to ensure 2 things: 1. The upstream routing device must have a route to your Virtual server subnet (using big-ip's client-side subnet self ip address as a next hop, floating self ip if you have a redundant pair of big-ips) 2. The Virtual server must be enabled on the big-ip vlan, where the client requests will come in - the default setting for a VS is 'enabled on all vlans', but you can limi it to specific vlan(s)