Whenever I am trying to preview homepage, this is the screen that I am seeing, but when I open the same page in the experience editor, the homepage does open, why am I not able to check the preview. And this happens not just with the homepage, but with every item in the Sitecore tree.
You have an error in file "WebService/Browse.aspx". This is Sitecore Rocks service.
As I see on your screenshot you are using Sitecore version 9.3. Parameterless constructor for LoggedInArgs was obsolete in sitecore 9 and completely removed in 9.3.
It seems that you use old version of Sitecore Rocks. Just install the latest version (or remove it at all if you dont need it and the error will disappear).
Sitecore Rocks versions 4.x are compatible with Sitecore 9.3
Edit #1 I downloaded and extracted Browse.aspx from latest version - it uses LoggingInArgs() without params. Looks like Sitecore Rocks bug.
Edit #2: I installed latest version of Sitecore Rocks on my clear Sitecore 9.3 to test this issue.
When I navigate to page preview in sitecore it works good:
It is because Browse.aspx should not be hitted from sitecore. This issue is reproduced only by opening browser from Sitecore Rocks in Visual Studio.
You can fix it manually by adding current HttpContext as a parameter. Open sitecore\shell\WebService\Browse.aspx and add Request.RequestContext.HttpContext as a parameter in line 43:
var args2 = new Sitecore.Pipelines.LoggedIn.LoggedInArgs(Request.RequestContext.HttpContext);
It is tested and works good for me.