Can I recite surah and verses of the Quran such as surah faitha surah tawheed and likewise.

Recitation of duas and Quran during periods is allowed. There are only 4 surahs in the Quran that have wajib sajdah in them. As per Ayatullah Sistani, only the verse of sajda should not be recited by a woman in her periods. It is said that Quran recitation during periods is makrooh- this means that the reward is less (not that it should not be recited).