Remember that this is a LAN protocol, and as far as I know, you cannot establish a BGP adjacency from the standby IP. If you configure BGP on the LAN interface, it will attempt to establish the session using the configured IP address, and you will end up having two sessions to the remote router. But if you have two sessions, you can use the methods I mention above to choose a primary router.
BGP does not have an active/standby feature: If your hardware doesn't support it (to fail-over to back-up hardware with the same IP and layer-2 addresses, as some firewalls can do), you are stuck with creating two BGP sessions.
1a) The secondary starts forwarding as soon as BGP detects that the adjacency is down. If it is a physical failure, it can be in a matter of milliseconds. But a silent failure on the neighbor (if the local interface stays up) will only be detected if the hold timer expires (by default up to 180 seconds). But you can configure the hold-time to a lower value.
1b) There is no aditional delay in forwarding traffic over the second link. The lower weight has got nothing to do with forwarding speed, and prepending AS numbers to the BGP routes being advertised does not slow it down either. Weight and the AS number count are only properties of the route, like 'metric' in OSPF or 'hop-count' in RIP, that influence which route is preferred.
2) If you leave all settings at default, some destinations will be routed over one link, and other to the second. If one of the links fail, BGP should converge (once it detects the failure, as in 1a above) to forward all traffic over the other link. If the links are the same capacity, this is recommended, but if the second link is only scoped for a back-up supplying minimum functionality, you will be better of implementing the configs above to force all rules over a single link, when available.
