Answering what I can:
In the file explorer, you mean? I don’t think so. Feel free to file a feature request.
Yes, see the Daily Notes plug-in settings.
This is not currently an option. Feel free to file a separate feature request!
I don’t think we can do this right now, but I’m not certain.
If “current folder” means the folder where the current note is on then it is possible!
Settings -> File -> New note default location -> “Same folder as the file is in”
I just noticed that there is an option to specify a folder where images and other attachments like pdf files go.
Ohh I misread. I thought you wanted to store images separate from other files. Sorry!