I'm going to have to disagree with you pfft. The AT Field is generated by the soul as explained by Kaoru Nagisa in Evangelion Episode 24 the Absolute Terror Field "...is the light of the soul!". It is not a mechanical construct but part of what all living beings possess. The Absolute Terror Field keeps us separate from each other, it stops our minds from flowing together, stops our body's losing physical form. During the Third Impact an Anti-AT Field was released, the result broke down everyone's AT Field, thus initiating Instrumentality.

The AT Field belongs to the soul, and the soul to it. The first two questions you posed can be answered easily.

Jet Alone was discredited by NERV because it was in competition for funding. They put on a good show too, until everything went wrong. The manufacturers of Jet Alone believed that they could overcome the AT Field problem. Obviously they were wrong.

The Lance may indeed contain a soul, but it definitely isn't the Second Angel. That's esteemed position falls to Lilith. Now Lilith isn't technically an Angel but then, neither are we humans and according to Misato we are the 18th Angel. The lance is not really understood fully. It was used on Adam during the Second Impact, and it originally came from the Dead Sea, other than that little is known.

Now onto your evidence that "purely physical" forces can defeat an ATF. I think this is where your problem lies. You are confusing neutralise with penetrate. The only thing that can neutralise an AT Field is another AT Field. There are many examples of this, but perhaps the best is in second episode two where Unit 01 neutralises the Angels field with it's own, and then proceeds to beat the crap out of it. The examples you sited, with the N² mines and positron rifles are only examples of extremely high energy weapons penetrating a deployed AT Field. The N² mines are the most powerful weapon that the earth possesses (other than the Evangelions) and in episode 6 they had to draw on the entire power supply of Japan to get enough energy to "penetrate" the Angel's field.

The Evas carry around weapons so they can use them on the Angels after they have "neutralised" their AT Fields. What you also have take into account is that different Angels have different strength Absolute Terror Fields, it is the same with the Pilots of the Evangelions. In the end Shinji Ikari has the highest Sync ratio and thus is the most powerful, he can deploy the strongest AT Field.

I know we are probably arguing semantics here, but there is a very big difference between neutralise and penetrate and it needs to be made clear that what you have said is not entirely correct.

Update to pfft's update...

I agree with everything you say in the first section of what you wrote. The ATF does play a dual role, though those roles are quite similar. Basically it keeps us separate from others, both physically and mentally and also spiritually if you will... The physical manifestation of the ATF is what we see when missiles deflect. I think it is a spiritual construct, a construct of the soul, which has physical properties when deployed. We humans don't know how to deploy our ATF's to take advantage of the more extreme physical properties. The Angels can, and the Pilots can as an extension through their Eva's, but that's about it. I don't think you could make a machine that could create an ATF, unless of course you could imbue it with a soul. Which is sort of what the Dummy Plug is if you think about it. A machine that can pilot and Eva and produce an AT Field, but then that begs the question, in the Evas, where does the ATF come from? The pilots or the Eva's themselves.

Now onto neutralisation. I agree if an ATF is neutralised it doesn't disappear; simply the physical manifestation of the ATF ceases to be. Also looking at the quote you put, it can be taken another way, especially if you take Misato's next line into account. Her line which comes directly after Ritsuko's is "That AT-field easily..." So I would prefer to think of that passage, as if it were all said by one person, going something like this:

Unit One expanding the AT-Field. It's neutralizing the phase space. No! It's eroding that AT Field easily!

Where the no is more an exclamation of shock rather than disagreement. Of course, like a lot of things in Evangelion, it comes down to your perspective and how you saw that scene. Neutralise is used other times during the series though. In episode 6 Misato talks about attacking "...without first neutralizing the target's AT field." In episode 11 when stating her plan of attack Asuka says " Defence stays here, neutralizes the AT field and also protects Offence from Angel's solvent liquid." Finally Asuka again remarks on neutralising an Angel's ATF in Episode 19 where is says "The AT field must have been neutralized. Why it doesn't get done for?"

I am probably just being pedantic but I think neutralise was used very specifically. It is different to what happened with an Anti-AT Field. The only good example we have on an A-ATF is in The End of Evangelion, just before everyone loses physical form.

The Anti-AT Field from Lilith... it's expanding further! It's materializing!

Anti-AT Field critical limit exceeded!

No...! If this continues, individual life-forms will be unable to maintain their separate entities!

I think the Anti-AT Field negates the AT Field completely, while other AT Fields can only neutralise them, and physical weapons can only pierce them.