What is a "safe" amount of amps to draw from this pack
Barring better information: If you know that someone is using safely using the battery packs for 7 minutes at 4.5 A, I think it's pretty safe to continuously draw 2 A – modelling the internal resistance as mostly ohmic, that's not even ¼ of the heat that gets generated at 4.5 A.

But you ask to verify the safety of your system, and that's impossible without a manufacturer datasheet guaranteeing that the batteries are operable under the conditions you want; no amount of "referene" usage is going to change that, as you don't know the lifetime / temperature / safety measures that other user (in your case, a consumer drone manufacturer) was assuming. And seriously, a USD38 drone isn't built to last. 

In fact, the information that the same battery pack is used in a least-cost drone means that these packs are pretty certainly assembled from the cheapest cells available at the time of manufacture – which means that you can make absolutely no assumptions based on your battery pack having the same label as some other pack.

Still, 2 A isn't "much" for a drone-targeting battery pack. It "should" be easy to build reliable battery packs for a load like that. But: since it's easy, it should also be easy to give you hard facts on the admissible current draw, and since you can't seem to find such, it negates this assumption.