Is it permissible to accept the second suitor, knowing that the first suitor has not responded to the marriage proposal for more than a week?

If the first suitor is not accepted, there is no harm in accepting the second suitor. This is not considered engaging over another's engagement, which is forbidden. Engaging over another's engagement is forbidden if the woman has accepted the first suitor. The proof for this is the hadith of Fatimah bint Qais, when Mu'awiyah and Abu Jahm proposed to her, and she had not accepted either of them. Then the Prophet, peace and blessings be upon him, proposed to her on behalf of Usama.