Hi Nitasali and welcome to the forum,
In case you are not aware, royalty-free does not mean 'free'. It refers to a form of licensing where you pay an upfront fee for the licence and you don't have to pay royalties. However, since you mention Unsplash and Pexels, you are probably referring to images which the copyright owner has released for anyone to use for free. However copyright still applies to these images, and it's just that the licence which comes with them is very permissive.
Take care when using sites like Unsplash or Pexels, and any other site offering free images. Be sure to record the details of the licence the site provides and the date you obtained the image from them. If, at a later stage someone claiming to be the copyright owner comes chasing after you, you need to be able to show that you downloaded and were using the image in good faith. For example here is Unsplash's licence:
License
Unsplash visuals are made to be used freely. Our license reflects that.
All images can be downloaded and used for free
Commercial and non-commercial purposes
No permission needed (though attribution is appreciated!)
As you can see they do not require attribution. I haven't checked the Pexels' licence but again you should familiarise yourself with their terms and comply with anything their licence requires you to do (or not do) with the image.
It's not necessary (and can be expensive) to register your logo as a trade mark in order to protect it. Provided that it can be described as an artistic work (however simple) then it should qualify for copyright protection. A lot depends on how valuable you think your logo is in your overall brand strategy. You mention that you provide a service rather than a product. In my experience personal reputation through word of mouth and goodwill are more valuable to someone providing a service, whereas strong branding can often assist in selling a product. As for protecting your website, make sure that you place a copyright notice on every page if that doesn't detract from the aesthetics, and certainly put one on your home page. This serves to remind visitors to the site to respect your intellectual property, although it won't prevent a determined person wishing to copy parts of it. If you are an artist or a photographer, for instance, do not put higher resolution copies of your portfolio on the site if you don't want them to be copied, and preferably embed copyright notices in any images that you have created. I am assuming that your probably aren't a photographer since you wish to use stock images from Unsplash or Pexels.
If you want to get more detailed advice on the pros and cons of registering a trade mark, find a trade mark attorney in your area and ask how much they charge for a simple consultation. You can find a Trade Mark attorney through the
Chartered Institute of Trade Mark Attorneys' website.
Also check with your local council or chamber of commerce etc to see if they provide free advice on marketing to small start-ups.