Hi Menachem and welcome to the forum,
A few issues you've raised here, so I'll run through them all for you.
In regards to not finding products to sell on eBay. What you have to realize is that eBay is the most saturated online marketplace on the planet, eBay.com has sellers from all over the world, shipping products from all over the world into the US and many of them are drop-shippers.
So if you want to compete on eBay with drop-shipping, you have to either get very creative with your marketing techniques or stay away from fast turn over popular markets and steer towards the slower turn over markets where the competition is more evenly balanced.
In regards to the bulk deal, that's what wholesale is all about. The downside is that you have to outlay cash up front and take the risk on being able to move all the stock, but the benefit potential is that you get more of a competitive edge with far better pricing. Drop-shipping saves you on having to take the risk and the upfront cash outlay, but then the down side is that you don't get the same price benefits, so you really have to decide which option is best for your market.
In regards to the shipping issue, I can't see any way out of this one. This really gets back to a lack of research on your behalf. You seem to have just jumped in without knowing what could be shipped to your destination and what was going to have problems. These are things you really need to research up front so this doesn't happen.
Sellers can't expect suppliers to do this for them suppliers don't know up front who you are selling to if you don't tell them. Even if you do tell them, it's not their concern, the seller needs to be aware of what they are selling and any pitfalls attached to those products.
I'm not sure why you informed eBay or the buyer that the item had already been sent when it hadn't, you've really created a massive mess for yourself now. Lots of mistakes made here, you really do need to consider if this is a business that you want to try and move forward with and if it is, you really need to treat it as a business and get some very firm research behind you before trying to move forward I feel.
I don't see any option for you now, other than to inform the customer that you will not be able to complete the transaction and will have to refund their money. The longer you delay that, the more chance of it blowing up to the point that the buyer gets eBay involved and then that puts your entire account at risk, especially if you are a new seller and I get the feeling that is the case.
The only thing I can suggest is to speak to Customs about the product. Get the correct information from them, see if they have a possible solution as to how you can get this into the country or is their something similar that can be cleared and then maybe offer that option to your customer, providing your supplier can fill that order of course.
Whatever you choose to do, do it fast, that's the best advice I can give you because this problem isn't going to fix itself and the longer it festers, the more harm it is going to ultimately cause you.
Good luck with it.