AirDroid is a impressive app, but I'm not able to access from pc to th SD content, only to the internal folders (also named sd card I think)
File Expert will give you both on-device, Explorer-like access to your files, and access over WiFi from your browser, an FTP client or Bluetooth. You won't need a separate browser-access app. It is well reviewed and free/no ads.
What do you mean with the "internal folders" are also named "sd card" seems weird to me. Maybe you assume /sdcard is a local folder? Which it isn't that's the location of your SD card's content.
Above, when you want to access your SD card's content in your PC, it have to be dismounted from the phone which will make apps installed on it inaccessible. Mostly you have to approve the dismounting of the SD card manually from your phone. I can imagine that when AirDroid is installed on your SD card it cannot dismount it because it has some necessary files on it.