Capt. Miller and Darby's Rangers. Now here we get in to some "rivet counting". Darby's Rangers were formed in 1942 in the UK, originally the 1st Ranger Battalion. 50 went ashore at Dieppe in August 1942 to get combat experience. After North Africa, the 3rd and later 4th Ranger Battalions were formed and added to the force. They were destroyed at Anzio early in the battle during late January and survivors transferred to the 1st Special Service Force. These Ranger units wore the black, white, and red Ranger scrolls like what is worn on todays Ranger Regiment soldiers (the scroll, not the tab from the school).
Rudders Rangers, the 2nd and 5th Ranger Battalions, which would go ashore in Normandy were formed in the US and then sent to England as part of the force for Overlord. These Rangers originally wore the Blue and Gold diamond shaped Ranger patch and later adopted the scroll.
I have read of one Ranger officer in Rudder's Rangers that had previously served in Darby's but he was relieved before the invasion. These two battalions had seen no action prior to June 6 and would have had little to no need for replacements coming in to the unit prior to the landing. Except perhaps to replace men injured or killed in training accidents. So possible, yes, probable...? you decide.
As far as uniforms go, the researcher did a great job there. For Overlord, the Ranger Force wore impregnated (an anti gas treatment) HBT fatigues with M41 field jackets and assault vests. What the actors wore in the movie. Helmets were marked as shown with the standard NCO or officers white stripe on the rear of the helmet as an orange diamond with the number of the battalion on the diamond on the back of the helmet as well for all Rangers.
Tank Busters? I think that was due to what they had flyable for filming. P-47s would have been the best choice, but how many of those are still flying today? Plus I do believe that Spielberg has a "thing" for Mustangs. Just a hunch, but look at "Empire of the Sun". And if you watch the special features Disc with movies he made as kid with a home camera near a desert aircraft boneyard. In the ETO, the few US P-51As were recon photo birds. Most Allison engined US P-51s flew in the MTO or CBI.