Issues after iOS9 update on my new 6s

Following the latest update on my new 6s, my iPhone is now having all sorts of issues. When I first got my iPhone from the store, it was working perfectly until the update.

1. half of my screen turns black while the other half is frozen.

2. iphone lag like there is to many apps running at once but only one app is running.

3. Maneuvering through multiple apps cause iPhone to freeze.

4. Key stroke sound lag

5. keyboarf doesn't respon to typing.

THere is is more but I just can't remember all of it.