Your R Square is actually positive, but it is close to zero. When this happens, adjusted R square maybe slightly negative. This is how adjusted R square formula is built to work. In fact, if R Square is <k/(n-1) , R Square Adj will be negative.
In your case, a negative R Square Adj. will occur when R Square <0.0013568. What a negative R square Adj. means is that the model terms do not help predict the response.
Does it estimate a model without the intercept?
No, it includes an intercept by default.