How to take Backup of BackUp DB in SQL Server 2012
Changing the IP of the secondary server shouldn't be an issue as long as you used DNS names in the log shipping configuration.

To answer your questions:


No you can't take a backup of a standby database, at least not with the native functionality in SQL Server.
As long as all the setting stay the same, there shouldn't be any impact. You can disable the copy and restore job before the change though.
There shouldn't be any impact as long as you used DNS names in your log shipping configuration. The only thing that I can think of is that you need to refresh the DNS cache of the primary server to get the new IP address.