Since neither HeidiSQL nor Notepad++ are Linux tools, a couple things you might consider:
phpMyAdmin - While this isn't great for larger operations (because it's web-based and memory constraints come in), it's really good for general DB operations. Make sure you secure it.
MySQL Workbench - Not quite as good as HeidiSQL or Navicat, but workable on Linux at least.
Sublime Text - Pretty good text editor (if you can't/won't use vi/vim)
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