First of all, while we all talk about chain stretch, chains don't stretch like the elastic on your Jockeys. Chain stretch refers to a wear process which allows the chain links to move farther apart at the pins. In this way it's more like the stretching of a freight train as the engine pulls the slack out of the couplers one by one when pulling out.

In any case a chain stretches less than 1/2" overall over it's lifetime.

Cutting you chain won't help, and might make it too short. Shift to the big/big combination and make sure you still have enough slack to pull the lower loop forward 1" at the bottom of the chainring. Then shift to the small/small combination and see that the RD is taking up all the slack. If it meets both tests it's fine.

As to the shifting. New chains tend to have different shift properties than old ones. Partly it's because the plates may be shaped slightly differently, but also because new chains are stiffer and closer fitting on the sprockets and so are less forgiving of any error. Take the time to fine tune all the RD adjustments and you should be OK.

If not, it might be that the hanger is misaligned, but you can cross that bridge if/when you get to it.