The latest I've read on Tribulus is that it may stimulate Leutenizing Hormone (LH), which may increase testosterone production in some men depending on individual deficiencies and other matters of biochemistry. Also, certain Tribulus formulas are superior to others. If you are one of the people lucky enough to benefit from it, then go right ahead. Given its nature, and the fact that there are no bans or restrictions on it, I'd say your "natural" status is safe.
As far as fats, yes: sex hormones are lipid-soluble cholesterol derivatives. Consuming healthy fat sources will help support optimal test levels. By optimal, I mean baseline. Don't make the mistake of thinking the more fat you eat, the more test you will produce.