Hi,
An Alternate port is a backup to a Root port that is connected via a different segment. An Alternate port will immediately transition to the Forwarding state when the Root port fails.
A Backup port is a backup to a Designated port that is connected to another switch via the same segment. This is not very common as you will need to connect a switch to another switch using multiple links on the same shared medium by using a hub.
See the the following link for further details
http://www.cisco.com/c/en/us/support/docs/lan-switching/spanning-tree-protocol/24062-146.html
Bridge Assurance is an STP extension that protects a network from any unidirectional link event caused by physical cable failure or adjacent switch control plane failure. Bridge Assurance is recommended and enabled by default on the vPC peer link but is not mandatory from my understanding. It is recommended not to enable Bridge Assurance on vPC member ports.
Please see the following on page 72 for further details.
http://www.cisco.com/c/dam/en/us/td/docs/switches/datacenter/sw/design/vpc_design/vpc_best_practices_design_guide.pdf
Hope this helps