You need a suitable non-null hypothesis to start with, too.

Suppose we're talking about a regular deck of cards, and someone says "the shuffler gives the first player too many hearts". That requires a different test to debunk/support it than the hypothesis "the shuffler gives the third player too many aces".

In other words, any claim that the shuffle is not random needs to include a testable assertion about the direction of bias it has, and allows you to make predictions about the next card with better than random accuracy.

The null hypothesis is that the cards are drawn from a uniform distribution, and if we only consider land/nonland as categories, it should be pretty straightforward to determine the probability of a sequence of draws under this distribution. Essentially it comes out to a weighted coin toss each time.

No, you can do a Chi-squared to test whether the distribution is significantly different from theory in any way.