

Yeah, it might be a good idea to check if the downspout isn’t partially clogged. I don’t know how high that building is, but around here, leaves can get in there every once in a while
If you haven’t checked yet, you might also want to see the abutment flashing (see #7 below) where that wall and roof meet, as water might be percolating in that area and getting trapped between the ceiling/drywall/insulation.

I’d also check the other flashings as well while you are at it and if that drywall and insulation on that affected area are damp, remove them for venting
I can’t tell too much from the pictures, nor feel and test the wood. You mentioned the plaster was soft, but what about the wood? Are there mycelium growth in it?
Check if the wood is dark, mushy, deformed, poke test it with a knife/awl/screwdriver, as wood with advanced decay will be soft and the probe will penetrate easily. How far does it go? How big is the beam? Do you know what kind of wood is it? Test in multiple areas
Tear up a more of the plaster to check how the rest of the beam looks like and test them. If it is less than 0.3 cm, venting might be enough
Another one is the pick test, where you insert the knife beneath the wood grain to pry loose a thin section of it till it breaks free. If you get a long linear splinter, itś most likely good, if it comes out as crumbly chunks or short pieces with a mushy sound, it is not ideal.
If you are in a dry season and no rain in sight, I’d clean both inside and outside areas to let them vent. Get a fan/dehumidifier/open windows in that room.
I also prefer breathable buildings, so you could use a more traditional breathable plaster, which allows water to easily evaporate over time, whereas concrete and all the PVA might help trap the moisture. It is typically made from lime and/or clay, sand, and water. You can also add fibers (horse hair or plant fibers) for strength

Smaller chainsaws can be more dangerous than bigger ones, watch out for kickbacks and learn how to use a chainsaw properly so you don’t mangle yourself up. Do not get fooled by the lack of noise from an electric chainsaw, they can still fuck you up
Having said that, yes, you’ll be able to handle them more easily. I don’t know enough about that brand to comment on it, but as you said, you already have a bunch of batteries available for it. Watch your footing and have an understanding of possible tension and compression forces on those limbs
But do you really need it? Are debris a common occurrence on your hike? I won’t deny chainsaws can be useful to have around, but you mentioned it would only be used on the trail and you already have a sawsaw
Btw, which blade are you using on your sawsaw? You might want to get a pruning blade if you are using a standard carpentry blade, as they can be way faster too