So in my weekly chest this week I got a +15 key from doing a +16 last week. If I don’t complete a +15 this week and let’s say I only did a +5, would my next weeks chest have a +14 or a +4 key in it?
It will contain a +4.
The key from the weekly chest is always 1 level lower than the highest completed (not necessarily timed) key of the previous week. If you open your weekly chest and do not do a key at all that week, then the following week your chest will not give you a keystone at all. Completing a M+ run at that point will give you a new random key 1 level lower than the difficulty you completed.
If you complete a 5 and still have your key in your bag you will get loot from the 5 but your new key will be 1 lower than what you did or what you have in your bag. Whichever is higher.