It is a good idea to shorten your feedback loop (as you said), so yes it probably is better for you to do 1 week instead of two. Saying that, look out for symptoms related to having a time boxed sprint and look toward general Lean principles for guidance. Also, the phrase "if it's painful, do it more often" might be applicable here, but that also means whatever problems/manual work you have every 2nd week today, you will get every week now - so automate.
To put it in perspective, the team I recently worked for ditched time boxed iterations all together in favour of a delivery pipeline based on features. They release the feature as soon as its ready, and don't wait around for a time boxed iteration to end. They now deploy to production multiple times a day, and release every feature when it's ready.
As for you other question, you are the best to answer what's most painful for you. If your team spend lots of manpower on infrastructure changes that can be automated with configuration management, it should probably be prioritised. If you have lots of manual acceptance testing that now will change from every 2nd week to every week, you might be able to automate some of that testing. This is a typical area where more frequent feedback loops might add additional strains on your organisation, and you need to look for ways to change the way you work and interact. However, you might be in a situation where you can increase your feedback loop with more frequent deploys, without additional strains. Note that the process your in now will bring pain points to the surface more often, and you need to be prepared to solve them.