The variations vs a separate listing is a debate I've read many times. What I would suggest is if the shipping is significantly different, then make separate listings. If you want to include it as a variation, then add the extra shipping cost in to the variation price.
For the time problem, you can adjust the date to ship after the purchase is made, and Etsy will notify your customer. However, I would suggest also including that information in the variation description. For example: Personalized (14 day prep).
Personally, I make separate listings for everything so that customers can see the price of the item in the search. I don't want them to feel like they were fooled into clicking by a lower price.
Finally, if you use someone else to help you make your items, I believe you must fill out your About page and list them as an employee. If it is a separate business, this needs to be disclosed to Etsy and you need to put it on your About page. I can't find your about page anywhere.