Adding whirlfloc around 5 minutes left in boil followed by a 5 to 10 minute whirlpool leave the majority of hot break in a nice pile in the middle of the boil kettle.
You can also add a hop back or randle with false bottom between BK and plate chiller to reduce BK material from entering the chiller. If you don't want to add hops to the hop back, use rice hulls per Tasty McDole. You can find several pictures of his setup with detailed instructions on his Facebook page or on the Brewing Network's forum.
In order to remove cold break and hop material that reside in the chiller, you can use an auto-siphon hooked up to the chiller to flush and back flush with hot water, PBW and StarSan after brewing in your kitchen sink. There are a few videos of this method on YouTube, and this methid works excellent for me. I flush mine in my laundry room sink, but you can get by using a 5 gallon bucket if you'd like.
To sterilize the chiller, you can recirculate during the last 15 minutes of boil.
I've never had an infection with a plate chiller, nor have I plugged chiller during cooling wort. I have cooled with plate chillers using gravity, but I use a chugger pump now since I recirculate my mash.
I love my plate chiller, and will never go back to IC. I recommend using DudaDisel and getting the largest surface area instead of multiple plates. If you're using gravity to feed, get the least number of plates to reduce the pressure drip from the chiller. I can cool 5 gallons of 190F wort in 5 minutes using the DudaDisel B3 - 23A 30 plate chiller. It's amazing. If I bought again I would get the 1/2" NPT fitting over the hose barb.
EDIT: I don't use a hop spider to block hop material and have no issues. I do use a pump to push the wort through the chiller, but I still had no issues the few times I chilled using only gravity, which is the only time it would be an issue. You'd have to have one hell of a clog if you can't push wort through your chiller with a March/chugger pump. I do feel I minimize my issues with a whirl pool to get a nice trub pile; I'll post apicture when I get home.