OK - first question is, do you actually want the eggs to hatch? Are you able to find homes for 17 Corn Snakes? If "Yes", read on....
I'm assuming that your female has been with a male at some point in the last year, so at least some of the eggs will be fertile.
White ones are fertile, shades of yellow/orange tend not to be. But the rule-of-thumb is to incubate every egg until it turns completely green with mould and collapses. The most unlikely specimens can hatch.
Eggs need to be kept in a range of about 77-85 degrees in order to hatch. They can go up to 90 degrees, but the higher end of the temp range seems to put them at risk of abnormalities (just anecdotal, no actual evidence). Unless your viv temps are very strictly maintained, then you'll need to move the eggs into an incubator to give them their best chance. Use the Search facility on this board to find out how to put one together.
Eggs should be supported in some kind of substrate like vermiculite or moss. This should be kept damp and to achieve that, most people use a tupperware box with the lid firmly shot. Some people have a few airholes, but I don't bother with mine. The boxes are airtight and seem to work OK as long as you check eggs once a week or so. Humidity is important to keep the eggs hydrated - if they dry out they can die.
Feeding a smaller mouse to your female would be helpful immediately after laying. As long as she keeps that down, then you can revert to her normal sized food after that. Depending on how much weight and condition she's lost, you might want to increase feeding frequency or the numbr of items offered, until she's back at her usual body weight. I give my females 2 adult mice at 10-14 day intervals and it usually takes them a couple of months to recover.
The female won't be at all protective of the eggs, so you're safe to handle her with the eggs in the viv (although as above, I recommend moving them out). In the wild, they drop 'em and leave 'em.
A bit of peace & quiet is usually appreciated after laying. Keep handling to a minimum for a couple of weeks, and when you do have to handle, be very gentle.
Mine usually stay put in one place after laying, so I get an extra water bowl and move it to within easy reach of them. They seem to like a drink when they're done.
I hope that helps.