On the subject of other navies reaction to what the FAA is doing, they will be quite small for some time.
After all, to observers eyes not much has changed yet. The Navy and RAF have had a big fight. Well, that sort of thing goes on in other militaries too, and all it means is someone else controls the navy planes.
The RN has managed to get the new carrier a year early and to a better spec than in OTL, but that isnt known, of course. In fact the RN carrier building program is restrained compared to, say, the USA, so its hardly going to cause much comment.
The internal reorganisation and improvements arent really obviously threatening anyone.
There will be other butterflies caused, but again, they wont be very obvious for a while, and may well get missed or at least minimised when the big war scare takes off in a few years.
The biggest change is in aircraft; the Stringbag is as OTL. A dive bomber and fighter will cause reaction when they come into service (and the RN will be pushing for that, especialy when the Luftwaffe is announced), but they have to be non-paper planes, and the RN isnt going to reveal their full performance. On paper, they wont look much different from US designs in progress at the time, and inferior to planes like the Me109.
On the subject of AA; its really too late to do much to improve the HA fire, that should have been started a few years ago, and in any case there probably isnt the money. The FAA will be pushing the risk assessment, certainly as soon as they look at whet their planes will do to a RN AA defence, but in OTL the RN didn about as much as they could regarding HA defence. Any changes will have to come in close in guns, pushed by the much greater risk assesment of the dive bomber, and that is much quicker to implement. The most likely changes are more pressure to get the 20mm and bofors 40mm under license and in production, and the other thing that wasnt done which is to do an improvement assesment and program on the 2pdr pop-pom. Which wasnt a terrible system, but was getting old by 1939, and an inprovement and modernisation would have reaped big rewards. The RN did have the heaviest AA fits in the world in 1939, and it will be improved.