There isn't a general rule to answer the more general question:
If I buy a bulk product (several pounds) and resell it in 0.5 ounce
packages (this is typically how it is sold, so this would be like a
“group buy” except I am fronting the cost)
Do I need to label the small packages with any text from the original
package? e.g. the logo, place it was manufactured, etc.
It depends upon the nature of the product.
The product is styptic powder which is a non-prescription powder which
is used to stop bleeding
The Food and Drug Administration imposes some labeling requirements if something qualifies as a "food" or "drug" which depends, in part, upon how the product is marketed. In the example given, it is likely that FDA labeling requirements would apply.
There are also different laws that require labeling of certain kinds of products that are outside of FDA jurisdiction, such as many kinds of chemical products. So, even if it is not FDA regulated, it is likely to be regulated by some other agency.
Also, the Fair Trade Commission (FTC) imposes some federal regulation on marketing and labeling of goods that are not required to have specific labels but must comply with those regulations if they do. Generally speaking, these regulations prohibit certain kinds of deceptive marketing and labels.
Apart from labels, it is also likely that the business of distributing an OTC drug (if that is what it is) requires the business to be licensed by the FDA in addition to labeling requirements.
Interstate transit and postal shipping regulations typically require certain kinds of basic disclosures about the nature of packages that are shipped in order to keep dangerous items out of mailrooms and delivery vehicles. As one example, goods containing lithium-ion batteries must prominently disclose that content.
Given the history of anthrax poisoning crime attempts and cocaine trafficking, the U.S. Postal Service and other common carriers are generally going to require declarations of the nature of any product shipped that is a white powder.
And, of course, state regulatory regimes and deceptive trade practices acts might also apply.
This is in the United States but potentially selling to other
You must comply with the laws of every country to which a good is sold.