Honestly, Luke not using his lightsaber is fine because he has two more movies to do that.
Concerning Han’s rescue, if anything should be cut, it’s the droids, without a doubt.
I agree. It’s a largely trivial concern because we have the other two movies to work off. Empire introduces the Emperor and the “Other” but the payoff is held to Jedi. The same could be argued applies to the lightsaber here.
That being said this article is very interesting. I don’t think I’ve ever been able to name a genuine flaw with ANH prior.