JohnnyColombia

I asked in the AA forum what happens on separate AA tix and it turns out they have a rule for it. It also appeared that the rule applies to AA/OneWorld flights where when booked on separate tix the carrier that causes the flight on the missed connection on a separate ticket is responsible for the rerouting.

Whether the above can be considered good for all OneWorld connections is anyone's guess.

My only experience is the other way around, take IB from LHR to MAD and then LA from MAD to LIM on a tight connection. I missed the MAD LIM segment and LA did indeed put me on the next available flight, however the next available flight in my fare bucket was 8 days later.

Anecdotally it seems that OneWorld carriers will be helpful but not very if you miss your connection. You should also bear in mind that staff of all airlines in BOG will be as unhelpful as they can get away with being without getting themselves stabbed in the eye with a dinner fork and also that the IB BOG MAD flight is always delayed anyway.

Edit to add: 3) Will LAN be able to check my bags all the way through to MAD, as both carriers are One World?

They are able to, but that is not to say that they will do. The reason I missed my connection in MAD above is that IB refused to check my bags all the way and it took 45 minutes for them to arrive at the belt. Although OneWorld airlines "can" check bags through to destinations on other OneWorld carriers on a different ticket, that is not to say they "will"

Although OneWorld claims that their alliance makes for easier connections and baggage handling, they do not expressly state anywhere that bags will be checked through to other OneWorld carriers on separate itineraries.