vServer doesn't respond properly (telnet+, browser-)

Check if you enabled snat on your virtual server, it is usual to select auto-map. If your servers don't have the big-ip as default route the server ends up sending the traffic to another device or straight to the client which does't recognise that connection (and reject it). For this to work you need aswell a self-ip in your 10.2.0.155 network.

The main use of self-ip's are monitoring. Big-ip devices use then to check health status of monitored devices. Other use is snat when you choose auto-map. There are other reasons (like failover and GARPs) but I think those are the most importants.

I hope this helps Kind regard