Water – how do i take the rain away from 2 sloping roofs meeting in the middle

If you don't have a problem with water pooling any more, the real answer is probably to have a professional roofer look closely at the roof both on the inside and outside. The problem with a lot of roof leaks is that where the water shows up in the house isn't where it comes in. Water has an annoying tendency to run along internal beams and such, then come into the house far away. You can go over any edges with new tar and hope you catch it but in my experience this approach ends up being like playing whack-a-mole, you patch and wait for it to rain, then patch more and wait more, etc.

So I would say if you can do it yourself, look closely at the underside of the roof as well as the outside. If you don't find anything, a professional roofer is probably in order.

The most important considerations are preparations and safety.

Make sure to fully evaluate the condition of the rafters at the top of the wall interface point. If the top log(s) are as severely rotted as you say the rafters are likely to be rotted at that point too. If they are rotted then you would not want to be jacking from the outside ends of the rafter tails. It may require jacking from the inside of the wall perimeter. In the end rotted rafters may cause you to have to deconstruct the roof structure so that be necessary rafters can also be replaced one by one and then re-assemble the structure.

You would need to consider adding some temporary cross ties as close to the bottom end of each rafter as possible. This will help to keep the rafters from spreading when you start the lifting process.

There will also need to be bracing added outside the walls from the orange pieces down at an angle to the ground. These braces need to be located both parallel to the rafters and perpendicular to the rafters. These can be anchored to posts dug into the ground. The braces will help prevent the roof structure from shifting laterally as it is raised up off the walls. One way the braces can be constructed is with overlapping lengths of 2x lumber that are clamped together. As jacking proceeds these clamps are loosened and reset to allow for the overall lengthening as the roof goes up and shortening as the roof comes back down.

Before doing any jacking do not forget to ensure that the roof structure is completely free from the chimney. It would not go well if the chimney were to impeded the roof movement.

Lastly ensure that there is plenty of help available during the raising and lowering process.