Hi CM and welcome to the forum, nice to have you with us,
Drop-shipping, along with other supply resource models, all have their advantages and disadvantages. What you've done here is hit upon tow of the disadvantages that the drop-shipping model has.
Shipping costs and shipping times can be a real issue for drop-shippers, so it's something you have to be vary wary of. Will customer's accept long shipping times?, well the obvious answer is that it will spend on the customer. However, in general terms, the longer a customer has to wait, the less chance you have of making a sale.
Product quality, a MASSIVE blind spot for you and if you're selling through a platform like eBay with a new account, product quality is something that can bring you down quickly. The only way you can gauge quality is to get access to the product and test it yourself. That will usually mean ordering one for a personal inspection.
Most don't do that for two reasons, they don't want to spend their cash on testing the products and they want to list multiple products, so the cost of personally testing everything is to prohibitive anyway.
You can increase your chances by reading supplier reviews on the forum and dealing with solid reputable companies, but that's about the best you can do without a personal inspection.
Shipping is of no concern for you, that's all taken care of by the drop-shipper themselves and if there are any import duties applicable on products, then those costs are the obligation of the customer, not you the seller.
Cheers