1. Can I place a kettle of cold water on the hotplate during Shabbos? NO it it reaches a temperature of 110 degrees F (or 43 degrees C yad sokedes bo) according to R’ Moshe. That is considered cooking. Others are even more stringent and consider a lower temperature as “Yad soledes bo.
2. Can I place a kettle of cold water on the hotplate five minutes before the onset of Shabbos? This is an “it depends”. Five minutes before candle lighting means that it will warm up for 23 minutes before sundown (shkia). If it reaches 110 degrees F during that time it may be ok. However, you would not be allowed to pour off any water during these 23 minutes. Better to put it on with enough time to reach 110 degrees (or higher) before candle lighting. Or boil it on the stove before this time and put it on the hotplate 5 minutes before candle lighting so it will remain hot.