Does changing the channel in which my wireless router broadcasts affects its performance?
And will there be any affect if I change the type of security protocol I use (WEP, WPA2 etc)?
Changing the channel may affect performance if there are a large number of WiFi routers already using the current channel in close proximity. In this case you may be able to reduce interference and retransmissions by changing channel, the channel number itself will it affect the speed of the router.
Encryption might affect speed on older routers, but I would expect any recent router to have more than enough power to be able to support the encrypted traffic over WiFi. I have seen older routers that could manage almost a third faster speed without encryption but I expect those days to be long gone now as the processors that are used now mostly have hardware encryption support built in. You may get a tiny bit faster by going with WEP encryption but as WEP is easy to crack I would not consider the loss of security to be worth a marginal gain in speed.
For best speed you need to make sure that your router is on a clear channel and if your devices support switching to 5GHz WiFi (which is typically clearer) then that might help.