1. No
2. No (See Ig”M OC 4:74 #23 where he discusses a hot water urn which like your hot plate doesnt have any adjustable knobs, nonetheless the water has to be “hot” prior to Shabbos He defines “hot” earlier in that teshuva as 160 degrees It wont get to 160 degrees on a hotplate in the 5 minutes before shabbos )
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