There is no best time but I tend to feed in the evening so I can leave the prey overnight and retrieve in the AM.
When I use hard boiled egg I just crush it put it in a baggy and put the mouse in it make sure it rubbed and sometime coated. I usually keep it in the freezer after that so I can reuse it instead of boiling an egg every week.
Same things with other scents, I keep those juices in little jars in my freezer.