Controller reported confusion between similar sounding call signs resulted in MVA violation and a CFTT event.

Narrative

Aircraft X checking; I verified they were ready for vectors to ZZZ as I noticed they filed. They confirmed and I issued a standard vector and told them to use caution for Aircraft Y similar sounding call sign. When Aircraft Y checked on; I did not tell them about the similar sounding callsigns as I was starting to get busy with other callups and an issue with their data block. Aircraft X was eventually descended to 110 and I began briefing the next controller on the weather at the sector while he was plugging in. (crosswind; turbulence; wind shear and pilots requesting runway XX)Aircraft X called the field in sight. I paused asking myself if that was Aircraft Y to which I mistakenly thought was the case. I cleared Aircraft Y for the approach. My expectation bias believing the aircraft on the straight in would call the field led me to miss the read back that Aircraft X read back that they were cleared for the visual approach.There was another aircraft on final for [Runway] YYL and a VFR RV aircraft overflying ZZZ at 95 Kts. I noticed Aircraft X descending and issued a climb and turn away from terrain thinking their descent and heading instructions got confused. They continued descending so I issued a low altitude alert and reissued instructions as I needed them turning soon to miss the VFR traffic and I needed them turning eastbound away from rapidly rising terrain west of ZZZ. The pilot later took Aircraft Y frequency change to the tower with the next controller as well. I recognize they were likely overloaded with tasks setting up for an approach after just recently departing a close by airport and being shaken by the mistakes we both made in communication failures.I will be more diligent in the future to listen for similar sounding callsigns taking the wrong clearances.Recommendation: The pilot and I both just need to pay better attention to transmissions when similar sounding callsigns are there. Its surprising to me that we both missed it when I even took the time to advise them of the similar callsigns. I need to stay diligent at all time.