1) Normally once a day snapsync is enough. If you have log sync enabled delphix will get archive logs and keep your snapshot up to date. Timing of snapshot should be dependent on your database as you may wana run it at time when your database is not too busy. Just like you do with normal backups.
2 Normally delphix gets archive log as soon as you perform "Alter system archive log current" (I am not aware of delphix internal mechanism but this is what I noticed on my systems). You can test this by performing log switch on source database and look at latest snapshot timeflow card. End timestamp value will change.
a) I would give it a little time just to make sure latest log switch make it to delphix.
b) For database refresh you don't have to stop activity on source database. You refresh your database from dSource not srouce database. They are independent of each other.
You can find latest log time using timeflowRanges
timeflow select db_name timeflowRanges
Timestamp in End point section is what you need.