Can we recite any quranic surah while our menses not by touching like if we hifd some surah like surahAl-Mulk in every night?
No problem in this whatsoever.
You can recite the Quran as well without any problem. The prohibition is only in touching the Quran with your bare hands. You can hold it by wearing gloves or through a barrier, like a cloth etc. The best would be to recite from your phone or any electronic devices.