I was reading a chapter on fadak in which I came across the paragraph from rudhutul kafi.
Firstly I wanted to ask is rudhutul kafi the same book- al kafi by Muhammad ibn Ya’qub al-Kulayni?

In addition to it I wanted to ask a question related to saying bismillah loudly in salah? Is it still recommended to say bismillah loudly in salah? If yes, Should we say it loudly even for those salah that are to be recited silently i.e zuhr asr.
And should we recite bismillah loudly only for surah fatiha or for the second surah as well?

Yes – Vol 8 of Kafi is titled Rawdhatul Kafi

Bismillah should be read loudly in all the prayers whether the Surah is read loudly or silently and for both Surahs.