Thank you for rescuing him! I am sure that you will take good care of him

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There are a few points were I can give you some advice.
The toenails can be remedied, but it is a lengthy process (no pun intended). You will have to visit the an avian vet with close intervals and let them slowly clip the claw back, as you cant clip it all in one go because of the pulp.
We have made a lot of progress,he lets me give neck scratches,takes food from my hand
This is awesome progress for a week, this could take a very long time, especially considering he's a rescue. As you've managed this, you can begin target training. See Michael's blog for more info:
http://www.trainedparrot.com/tamingTargeting is a great tool, with which you can get your bird to go in and out of his cage, and also the travel carrier eventually.
I doubt you will have time for that before tuesday though, and I will leave it to others as to how to best handle that. Unfortunatly you might have to grab him and just put him there, it might dent your relationship, but they get over it. There might be some blood loss involved here

, amazon beaks are nasty (I know).
Also, please consider letting him regaining flight. Since this is an older bird you will probably have to teach him to fly, which Michael has some excellent advice on how to do. Your bird will love you for it, and will be much healthier and happier.
I would like to point out that some old school vets might say a clip is good, but they are uneducated as to the benefits of flight and have a very old and undeveloped way of looking at parrot keeping. Dont listen to people promoting clipping, they almost never have the birds interest at heart, but rather their own convienence (though very few admit it). There are VERY special occasions which COULD merit a clip, but they are very few and far between, and in almost every possible situation its better to have a flighted bird. Check out this article, and dont be offended if you are pro-clipping, but read it through anyway and consider it:
http://www.trainedparrot.com/clippingGreat place BTW
Please stick around. You've shown amazing progress in a week, and youve saved that poor parrot from a bad place. We want to hear about your continued progress!