Yes: You may register your original arms here with the caveat that they should not be the same as someone else's arms. The idea of arms is that they are exclusively specific to you, the armiger.
(They should also conform to long-held Heraldic tradition, and be blazoned properly.)
No: In accordance with our Terms in Section 7.2:
§7.2. Surname or Family Arms: The Society does not accept commercially available "surname" or "family" coats of arms typically found in genealogical forums, search engines, or sold by unscrupulous vendors. Basically, Lord Lyon, the College of Arms, the Chief Herald of Ireland, and the Canadian Heraldic Authority all agree that strictly speaking, there is no such thing as a 'family coat of arms'. A grant of arms is made to an individual and may extend to his or her descendants, but not to a family surname.
No: In accordance with our Terms in section 7.4:
§7.4. American Armigers and the idea of Nobility:
For American Armigers, our Society accepts only blazons and emblazonments of basic achievements for assumed arms: shield, crest, motto, and badge. The Society does not accept blazons or emblazonments of personal assumed arms which describe supporters, mantles, robes of estate, or helm and crown configurations that are emblematic of nobility or any other status inconsistent with the American Principles of Equality.
No: Again, in accordance with our Terms in section 7.4:
§7.4. American Armigers and the idea of Nobility:
For American Armigers, our Society accepts only blazons and emblazonments of basic achievements for assumed arms: shield, crest, motto, and badge. The Society does not accept blazons or emblazonments of personal assumed arms which describe supporters, mantles, robes of estate, or helm and crown configurations that are emblematic of nobility or any other status inconsistent with the American Principles of Equality.
For more detailed information, please read through section 7. User-Submitted Information in the Terms and Conditions page.