Can I get a visa for both Hong Kong and China there at the embassy? (I'm from Nepal)

You can apply for a China visa from the China embassy in Kathmandu, Nepal.

As for the Hong Kong visa, according to the rule, The Nepalese applicants, if apply for visa to visit/transit HK for the first time, should apply directly to the Immigration Department of the Hong Kong Special Administrative Region (HKSAR). HK visit visa (3 months valid, double-entry, 14 days each entry at most) could be issued to Nepalese ordinary passport holders traveling on business purpose.

When you go to the embassy to apply China visa, you can enquire the procedure of Hong Kong visa.