Not long enough in this house! If the lids on properly it should last a good while - use it up over ice cream or in coffee or in a cheesecake etc. My sis-in-law had a bottle open from Christmas to the following Christmas and it was fine - so can't tell you more after that!
Depends on how many you have at the party, about half hour ?
Despite being cream, it has a high alcohol content and so seems to keep well. Certainly I've drunk Baileys and copy-cat concoctions years after they were first opened, with no ill effects. So if it smells and tastes ok it probably is. And anyway, you'll soon find out.
Baileys recommend consuming an opened bottle within 6 months. It should also be kept away from sunlight and cool - your fridge is ideal. It also doesn't like changes in temperature, so it's best kept cool all the time. If it looks and smells OK, it will be safe to drink, though the flavour may not be at its best after a few months.