1) "Think like a raindrop". Where can water come from? Where can it go? Where does it accumulate? Use a moisture meter on the ceiling below to try to map out areas of higher moisture content. What happens with leaks, generally, is the insulation gets wet and is slow to dry in an enclosed space like a floor/ceiling. The wetness of the insulation will lead to wetness on back of the drywall.
Now this only tells you so much, because one leak can soak a lot of insulation, but it can tell you generally where the problem areas are, like the south wall, or the west wall, etc.
Where does the wind driven rain generally come from in your area?
Also, penetrations. Any penetration in the (supposed) waterproof floor/roof/etc is suspect. Deck railings and posts, for example.
Also, how is the patio constructed? Is it a torch down membrane with a wood or paver wear surface, or one of those roll on "waterproof" membranes? I would be suspicious of the latter
2) The best way is to remove the floor entirely, remove any rotten framing, wet insulation, etc, and rebuild it. If it has leaked long enough this is the only option. I have custom stainless pans built for all exterior doors that aren't covered by a roof, and if I'm near the ocean where we have strong wind driven rain these doors get pans even if they're under a roof. I'll put 30# felt (tarpaper) below the pan, the same 30# felt over the sheathing vertically (cut into long rips around 8" wide) that lap over the pan, install the door, then another layer of felt over the door flange. This is for a slider, a swinging door is done with one layer not two. The pan is constructed with a short vertical plane (1/2") on the sides and towards the building interior, and it laps over the stainless flashing or vertical part of the torch down membrane below. You work from the bottom up so everything laps properly, again "think like a raindrop". You wouldn't believe how many times I've torn apart walls and found the lap done backwards.
The second best way is to remove the ceiling below, but this obviously doesn't address the issues in waterproofing above, but sometimes it's necessary to asses and repair any damage. The problem here is that often a leak above will show itself in a different location below. Another issue is that it creates a big mess in the living area.
3) I have this one
https://lignomatusa.com/product/mini-ligno-ed-pin-moisture-meter/ I have been happy with it. I use it on wood to determine moisture content, in drywall to try to follow leak patterns behind the walls, and firewood.
You can take a deep dive on the differences but the bottom line is they both work. I prefer the simplicity of the pin type, personally. I trust them more, which is fully subjective. I also use it more as a "relative" tool, as in, what is the MC in this area, or this board, compared to that area or board when trying to chase leaks.
Finally, these types of porches, decks, etc over a living area are problematic. I build on the coast so they're really problematic. If they don't have roofs they're even more problematic. It's not just the floor waterproofing that has to be done right, the walls do, too. Any mistakes in the wall plane can get right past the "perfect" floor waterproofing and show up in the ceiling below. I would consider them like a roof, with a life expectancy of 30-40 years if theyre done right. And so much of what I've seen in modern townhouse/condo construction is far from "done right" in terms of exterior details.
