The use of intellectual property(images, text, ...) from a third party without consent is simply not legal in europe.

https://www.gov.uk/topic/intellectual-property/copyright

https://www.gov.uk/guidance/exceptions-to-copyright

Base on that, why Google (apart from being Google) and DuckDuckGo are able to legally list links (with images and small descriptions) to products in their shopping/products sections of search.

The owners of the sites, not the internet, can provide permission. If it is a question of not wanting to do something illegal but paying for legal advice does not make economic sense, then that's a sign that the larger project may not make economic sense. If there is no legal advice up front and the project turns out to create legal liability and be uneconomic, there is a non-trivial chance that you may wind up paying for legal advice down the road for a project that does not cover the cost.

Good luck.

As a general rule of thumb (UK, specifically) asking for implicit permission will either get a standard no or no response at all.

However, if the information is reasonably accurate and links back to the merchant's site it is very unlikely they will complain, especially if the links are 'follow' and not affiliated (not that it would make much difference anyway).

You might have a fair use argument in that you're combining multiple data sources into something novel. Similar to how video compilations can be fair use. But IANAL and I don't know if that's been tested in court.

I remember there was a law passed in 2005 in the US that added additional protection to company databases and the data they contained.

Look at robots.txt first.

If the website owner says there DO NoT CRAWL, uou cannot use that data.