Can his spouse put in an I-130 petition and apply for adjustment of status, etc. since she is a citizen and he did not enter the country illegally?

Generally, a foreign national who entered the U.S. lawfully and with inspection (such as with an H4 visa), and who then became married to a U.S. citizen, may succeed in a marriage-based adjustment of status application to become a Lawful Permanent Resident (to get a "Green Card"), notwithstanding that the foreign national spouse became out of status and successfully applied for DACA. Of course, there are many other details that determine eligibility. It would be wise for your friend's son and his spouse to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.