Q: my mac dont recoginze my iphone with usb (original) connection. how to import few photos without using itunes sync?

Hello noa.kva,

I understand that you are trying to import some photos from your iPhone, but it does not show up on your Mac.  Let's go over some options to get that working for you. 

Now the first thing to try is using Image Capture to import the photos. This is an app that is already on your Mac in the Application folder. Take a look at the article below for steps on importing using Image Capture. 

Image Capture: Transfer images and other items from your device
https://support.apple.com/kb/PH17894

Now I don't want to ignore the fact that your iPhone does not show up on your Mac. Take a look at the second article for some troubleshooting option to get that working. 

If you don‘t see your connected device in iTunes for Mac
https://support.apple.com/en-us/HT203979​

You also mentioned that you are unable to use AirDrop. Take a look at the final article to look at the steps as well as the requirements to ensure that you can AirDrop your pictures to your Mac. 

Use AirDrop to send content from your Mac
https://support.apple.com/en-us/HT203106

Let me know if this help.

Take care