There are no major events during that time, but maybe some niche things going on. I did see a 10k run and a swim event, there are some music festivals (Jordaan Festival, Amsterdam Fringe Fest), Sep.14 and 15 there are some museums and government buildings that are open for entrance free, but overall it seems like there are lots of small things going on if you have an interest.
The weather can range from cool, maybe a bit rainy, to warm. I bring a light fleece and a rain shell for that type of weather, maybe a few layers.
If you are interested in craft beer, I can help with that in another post, same if you want to taste some of the local Jenever (gin like liquor)
There are lots of towns within easy distance from Amsterdam; Haarlem, Leiden, Delft, Den Haag, Rotterdam, Utrecht, Alkmaar...just to start. They all have museums, botanical gardens, canals, parks...depends on your interests which are best.
Trains are a breeze to use, simply use your credit card or phone to tap in and out, download the app to help figure out the best train for where you want to go.