1. Yes, you can worship Greek and Roman gods. Roman religion existed prior to Hellenic influence though it did become quite Hellenized. There are many similarities but there are still distinctions between the two religions with some gods that were equated with one another but it's not so simple as "X is also known as Y".
2. Absolutely. Much of what's found in Neopagan blogs, videos, and social media is Eclecticism and is not authentic to traditional pagan practices. Even the public perception of Wicca is grossly skewed. Regardless, while magic existed in the ancient world, the modern definition is different from that of ancient cultures. And in Hellenism, for example, not only was magic or "witchcraft" not a part of religious practice, it was considered hubris.
3. If you're interested in learning Greek and Roman traditions, you're far better off sticking to ancient and academic sources. Fortunately, a great deal has survived of Greco-Roman religions and has been researched for centuries so there is an abundance of reliable information, much of it available for free and online. (See examples below.)
4. Hellenic polytheism is known by a few names: Hellenism, Olympianism or Dodekatheism. Roman polytheism is referred to as Religio Romana or Cultus Deorum.
First, don't rely on social media for your primary research, there's far too much pretend and incorrect information to wade through. Sometimes there are useful blogs by modern practitioners but those should be supplemental to the other material. Of the very few groups that exist, Labrys.gr in Greece has published a book on setting up a modern household religion, called
Hellenic Polytheism: Household Religion. They also have a few useful articles on
their website. For Roman polytheism, there's the
Religio Romana Handbook from Nova Roma which is available online for download.
Anyone who has the internet has access to a wealth of ancient/historical information as there isn't a museum or university that doesn't have an online presence. Many scholars and professors offer research papers online at places like Academia.edu, Google Scholar, and jstor.org.
Many useful books are in the public domain and can be found (and downloaded) from places like:
Google Books
Gutenberg.org
Archive.org
plus there are many sites dedicated to Classics like:
Theoi.com
Perseus Project
Lacus Curtius
(to name just a few)
Hellenic and Roman religions are some of these most well documented and studied ancient polytheistic religions, the information available to us is exponentially greater than other polytheistic religions that have little in the way of surviving ancient records and have to rely nearly entirely on second-hand, biased accounts by latter-day Christian writers. tbh, there isn't much a person developing their practice can't find, especially if they're looking for basics.
