Reinstall MacOS Sierra I've already installed macOS Sierra.
But I've also performed a "general" cleaning and I suspect some files were gone.
Now the whole system is slow, some things doesn't behave the way they used to.
Is it possible to download again macOS Sierra from AppStore and simple reinstall it?
I mean, install macOS Sierra over macOS Sierra that is already up and running (not so well...).
Thanks a lot for your help.
The short answer is YES.
It is possible to install Sierra over Sierra.  The procedure is no different than installing one OS over another.  Personally, I would wipe/format my target drive (using Disk Utility) first.  Be sure you have a backup of anything you don't want deleted forever.
There are a couple ways you can do this:

Internet Recovery (Hold Command R while booting)
Download Sierra from App Store and create a USB installer (preferred)

Both methods will utitimately work identically once you have the installer loaded.  With option 2, if you choose to restart or want to do it all over again, you won't have to download the image repeatedly.
To create the installer, you just need an 8GB or larger USB flash drive and the installation image.  Once downloaded, format the USB drive with a GUID partition, Journaled and call it Sierra (or something easy for you to remember).  Then, issue the following command:
sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/Sierra/ --applicationpath /Applications/Install\ macOS\ Sierra.app/ --nointeraction

Re-install to your hearts content.