After doing some searchingand after I waited some days for others to chime in, I come to the conclusion that:
Both (1) and (2) are not possible.
On stackoverflow there's a discussion of (2) herehere and someone suggesting a workaround herehere which essentially means to close/award the original bounty, and then award a second one.
According to Meta on StackExchangeMeta on StackExchange a question like mine which affects all sites, should probably be hosted and asked on meta.stackexchange.com.
Let me know by commenting or providing more answers if you disagree with my conclusion.