If I delete photos from my laptop that are uploaded to flicker, will I lose them everywhere?
As Hovsep mentioned, the pictures on your laptop have nothing to do with your Flickr pictures except when uploading the pictures. When you upload your pictures, you are sending a copy of the pictures for the Flickr servers to store and share. Since it is a copy, it is, in a way, backed up on Flickr, so you can edit and change or delete the pictures on your computer, but the copies that Flickr has will not be affected. You would have to log into your Flickr account and manually delete the pictures from your account to remove them from Flickr.
Thank you both very much for your responses, I truly appreciate them.
if synchronization is one way so your photos will be uploaded to your Flickr account and if you delete your photos on laptop they will be available on Flickr, you can check this by deleting couple of photos on your laptop and check on Flickr for them.