One site offer download many images but in that site haven't any terms. When I asked: Is this really free? They answered: Yes it is, our website is absolutely free. Their images has watermark. Can i download them to my computer, using Photoshop edit - remove watermark to use for my site / my onw purpose?
I would double check with them to make sure they don't mean, free to look at. Even a lot of stock photo sites require you pay extra if you want to create derivative works. Especially if you're planning on selling it, like headers or templates.
You need permission to use any photograph - it doesn't matter if they say copyright or not. You cannot remove a watermark without permission - which I doubt they will allow. Some sites give away images with watermarks to advertise their sites. Removing the watermark would break the terms of usage. Also be aware that even if a site says "free images" there is usually terms of usage. If the site didn't own the rights to the images, you are liable for damages to the copyright holder. That is why you need to be careful of the source you get your images from. Using a site like istock is a small price to pay.
Yes, you should not remove the watermark - the images are protected for browsing, but will be watermark free when you download them as the site want you to. You can get free stock photos at http://www.freerangestock.com that have no watermark once you register and download. You can't resell or use the images on items for sale, but you can do most other things. If you use them in a template, you need to provide credit in the footer of the page. Otherwise, no credit is needed.