is link / href with just parameters (starting with question mark) valid?

Solution 1:

Yes, it is.
You can find it in RFC 1808 - Relative Uniform Resource Locators:

Within an object with a well-defined base URL of
Base: <URL:http://a/b/c/d;p?q#f>
the relative URLs would be resolved as follows:

5.1. Normal Examples

?y = <URL:http://a/b/c/d;p?y>

RFC 3986 - Uniform Resource Identifier (URI): Generic Syntax restates the same, and adds more details, including the grammar:

relative-ref  = relative-part [ "?" query ] [ "#" fragment ]

relative-part = "//" authority path-abempty
             / path-absolute
             / path-noscheme
             / path-empty     #; zero characters

Now, that is not to say all browsers implement it according to the standard, but it looks like this should be safe.

Solution 2:

Yes - and it will hit the current url with parameters what you are passing.

It is very convenient to use in situations where you want to make sure you do not cross current page/form boundary and keep on hitting same ActionMethod or whatever is listening with different parameters.