Suppose i have a wireless router. My PC is connected to the router with a wire. My PC has no WiFi adapter/card. I have an android phone connected to the router via WiFi. And i have NO INTERNET CONNECTION. What is the best android app to transfer data between phone and PC, in this situation?
My own recommendations would be to use either "ES File Explorer Pro" (paid-for Pro because the free one is VERY unpleasant nowdays), or "Total Commander" (which is free and VERY capable), but for the latter you also need to install the LAN module, since that is not included by default in the main app. But as that module is also free, it's no big deal. I started out with "ES File Explorer Pro" long ago, and only recently started using "Total Commander", so I tend to install both on my Android devices. Both have some great advantages and some quirks of usage, so which to use is mainly a matter of personal usage preferences. One warning though: If you use "ES File Explorer" (free or Pro) to backup some app config files to any external media (USB-HDD, LAN fileshare, whatever) then the program may add a ".txt" extension to any files that have text content, even if they are NOT originally stored with such a filename extension. This means that if you later need to restore those files to the Android device, the apps that used those files will not recognize them, unless you rename the affected files to remove that unwanted ".txt" extension. I became aware of this problem after attempting to restore folders containing configuration files for a large number of emulator games, only to find that all those configurations were being ignored by the emulator apps, simply because all 'whatever.ini' files had been renamed to 'whatever.ini.txt' by "ES File Explorer" in making the external backups. But apart from that horrible bug (a by-design bug!) "ES File Explorer Pro" is one of the most competent and convenient file managers available, with great compatibility across Android devices of all kinds.
A little late to the party, but why not just connect the device to the PC via USB to transfer files. It's what I use all the time to sideload APKs, grab screenshots etc.