PrintScreen Doesn’t Work in Context Menu – How to Fix

I don't use Sublime and so can't comment on that aspect.

However, for Filezilla and with Adwaita-dark, I see what you report:

When using Blackbird which is another dark theme, Filezilla looks like this:

To install Blackbird, run

sudo apt install blackbird-gtk-theme

I suggest you experiment with other dark themes if you don't find Blackbird satisfactory.

And, if you want to use Adwaita-dark for all other programs, but just want to run filezilla with Blackbird, create ~/.local/share/applications/filezilla.desktop with the following contents:

[Desktop Entry]
Name=FileZilla
GenericName=FTP client
Comment=Download and upload files via FTP, FTPS and SFTP
#Exec=filezilla
Exec=bash -c'GTK2_RC_FILES=/usr/share/themes/Blackbird/gtk-2.0/gtkrc filezilla'
Terminal=false
Icon=filezilla
Type=Application
Categories=Network;FileTransfer;
Version=1.0

As for whether what you see can be fixed, it appears that the GNOME team is just waiting for gtk2 to die. See /usr/share/themes/Adwaita-dark/gtk-2.0/hacks.rc. From there:

This file contains horrible hacks to make this theme work with some programs This is mostly due to the limitations of gtk2 but sometimes its the fault of the programs themselves. Not going to point fingers.

Either way, it's a WONTFIX for both, hence this horrible file.

To my mind, the solution is to use another theme that meets your requirements. Of course, one could always approach the developers of applications and ask them to make their applications play nice with Adwaita-dark. But I suspect they won't be overly interested.

Edit: The fuzzy effect is due to the application of text shadows. Text shadows, if used properly, can ensure text visibility against a variety of backgrounds and are often used for text belonging to desktop icons, given the fact that users may want to swap backgrounds, and hence background colors, at will. The downside is the fuzzy effect. You can read more about text shadows in Can text shadow enhance readability?.