We usually incorporate into a batch script. It works with either local or domain users. In our process, we pipe in a decrypted password. This also assumes that the user you are running as has appropriate rights on the target machines (typically via GPO).
Generally this works well. There are some known issues with certain version of PSexec and certain OSes. You may need to experiment using either older or newer versions to meet your needs.
Not directly. On Windows, an alternative way (in addition to the psexec approach already discussed) we have found is to create a scheduled task to run with whatever credentials are needed. Credentials for either a local or domain account can be used.