Regarding website

Gmail or mobile numbers are sometimes protected (either by design, like Google won't give you info on users, if users don't wish to let it be known or never filled in anything identifiable, or because it's a burner SIM)
Just ask your question here though. You're pretty vague as it is now.

Thank you. I just first asked in general and actually you gave me an answer.

So is it possible and how to find out if the website is spam or not?

Better to have the actual site URL for testing + looking at various blacklists.

Tough to even know where to start without a URL.

is it possible and how to find out if the website is spam or not

For fake website

1. Goto https://www.whois.com/whois/
2. Paste the URL of the website in the search bar
3. Look up the results and you will see who is the website owner and when the domain name is registered and when the registration will be expired. Normally, a fake website will be registered within last six months and the registration will be expired on its first anniversary.

For spam.

1. Use an email client which can show the full email header, like MS Outlook
2. Copy the full email header
3. Goto https://www.whatismyip.com/email-header-analyzer/ 
4. Paste the full email header in the search bar
5. Look up the results and you will see which country, ISP and organization for the source of the email.

Below is the results for an email from Microsoft Event Registration.  

The email source IP address is: 52.54.83.49
The email source IP host name is: mail2.certain.com
Country: United States
City: Ashburn
Area Code: 703
Latitude: 39.0481
Longitude: -77.4728
ISP: Amazon.com
Organization: Amazon.com

Below is the results for a spam.

The email source IP address is: 219.137.118.233
The email source IP host name is: 233.118.137.219.broad.gz.gd.dynamic.163data.com.cn
Country: China
City: Guangzhou
Area Code: -
Latitude: 23.1167
Longitude: 113.25
ISP: China Telecom
Organization: China Telecom

Finally, you can use email source IP address to find out whether the email source IP host name is a spam host.

1. Goto https://mxtoolbox.com/blacklists.aspx
2. Paste the email source IP address in the search bar and you will see the results.

As others posted, your question and info you provide are commonly different.
A website is determined by the URL.
Commonly an email address or a phone number would commonly not lead to websites....

If you received an email or an Sms with a UR from an unknown source, I would suggest it is commonly a spam.

Likely the test arnold mentions is best.

If you received info about this site from unsolicited mail or text message, best just delete it, rather than wasting time on research.

If you try researching 100% of all spam received, every day, then your only life activity will be spam research.

Thank you for the information.
I should explain my question which I understand was not so clear. Sorry for that.
I found the website via google. The email  address and mobile  is given in that website.  I contacted by that mobile.
When I started to suspect  that the website can be fake/spam I tried myself to find out using the website's URL, but  I did not manage . So in addition I tried to found out  the owner by the given Gmail or mobile,  as I suspect that they are fake and I wanted to know with whom I really had contact. As I could not solve this I decided to ask help here if it is possible to find out.

With the clarification, you can use the phone number in a Google search and see whether others have reported it ..
Context is important. But understood the nature of the site may be suggestive.

The searches often are populated by "fake" or misleading entities on the searched info. Depending on the search topic one has to view the responses skeptically based on the underlying sites.
I.e. Well known entities versus ....

Happy New Year!

Any update?

You asked, "So in addition I tried to found out  the owner by the given Gmail or mobile,  as I suspect that they are fake and I wanted to know with whom I really had contact."

There's no way to do this anymore as all whois data is obfuscated from GDPR requirements now.

You can only contact a site owner through a site now.

If you have a large budget + this is important to you, hiring a Private Investigator will be your next step.

Or... you can just delete the SPAM + move on.