WinSCP matches all your requirements.
Graphical: Yes – There are two alternative interfaces:
Feels like a Windows explorer window: Yes – One of the interfaces is explicitly designed after Windows File Explorer.
Supports drag and drop: Yes – Both between file panels and between other applications.Uploading via ...
I have used the 3 following FTP clients during the past years so here is my feedback:
WinSCP: the one that I currently use. There is a portable version, just one .exe file (and the .ini file for configuration). Don't forget to turn on the "Explorer" interface:
View > Preferences > Environment > Interface > Explorer, which is (IMHO) handier.
Benchmark: it ...
WinSCP allows automatic updates to donors. So it's not "gratis". But it is possible and only $9 donation (or equivalent) is required.
FileZilla allows automatic updates to anyone (on Windows). See How to automatically update FileZilla?
No, such a software doesn't exist. It's hard to prove a negative, but FTP is a file transfer protocol, so it transfers files from the server to the client.
Instead, you should be looking for editing software on the server. Some hosting control software has this built-in, e.g. cPanel offers an HTML editor.