It's been a while since I've seen the show, and can't think of these scenes off the top of my head to comment on specifically. My understanding is that Marines of the time relied on their attached Navy Corpsman (basically the squad medic) to provide combat lifesaving, but hopefully someone with more expertise on that topic can weigh in.

What I can address is the tourniquet issue. Because applying a tourniquet wouldn't have been basic lifesaving treatment during WW2, and just applying pressure dressings was usually the best they would do.

Tourniquet use has changed considerably over time, as understanding of lifesaving treatment has changed. While modern combat lifesaver training (and first responder training in general) encourages the use of the tourniquet for major bleeds in the extremities, this is largely thanks to recent advances in our understanding.

To quote "A brief history of the tourniquet", by Norman M. Rich, MD, et al:

The use of tourniquets in the ongoing wars against terrorism in Iraq and Afghanistan represents one of the true advances in battlefield medicine of our era. At the beginning of these conflicts, the use of tourniquets on the battlefield was largely frowned upon because of experience from previous wars and lack of modern data.

WW2 was one of those previous wars where widespread use of the tourniquet was frowned upon, largely due to experience with their misuse during WW1. In the US military, tourniquets were indicated as a last-ditch measure, only after pressure dressings had failed. The directions on the US-issued tourniquet even warned not to use them unless absolutely necessary. These tourniquets were only issued to medics - the average soldier only carried pressure dressings and would have been advised not to try to improvise a tourniquet.

When tourniquets were used during WW2, frequent misuse leading to preventable limb loss resulted in a stigma against their use arising. Many units switched to indicating tourniquets for only actively spurting arterial wounds, and as far as I can tell, this remained their advised use in the US military until Afghanistan changed that.