1. The subject of strategy is taught by the Army at the 0-4 level at CGSC.
2. It is also taught at the senior service school.
3. How to actually make strategy really isn't taught or not very well. I defer on this to my recently retired colleague from the Army War College, Dr. Gabriel Marcella.
4. Grand strategy for the US is made (or the responsibility of) the President with the advice of his NSC. It is published as the National Security Strategy of the US supposedly annually according to the Goldwater-Nichols Act. Because it is unclassified, it is inherently a partisan political document - some more so, some less. (The best of these was the final one published by the Budh 41 Adminsitration.) The NSC includes the CJCS as a statutory advisor; therefore, the military has appropriately input to US grand strategy. Note that the NSS is, in reality, a bureaucratic product so the Joint Staff and OSD are players. Key players from both as well as the NSC staff often wear military uniforms.
5. Much of what passes for strategy is not. What usually gets short shrift is the necessary focus on resources. Failure to include a detailed analysis of the resource leg of the stool means that strategy is little different from policy.When I was Chief of Policy & Strategy in SOUTHCOM I produced Gen Woerner's last Regional Security Strategy and Gen Thurman's SOUTHCOM Strategy. The difference was in the resources component. We did not do a very good job on it for the RSS and Gen Thurman insisted that we make the resource leg of the SS as complete and important as the objective and COA legs. Bottom line is that strategy seems easy but it really is hard.

Cheers

JohnT