Could believers who had been baptized cast out demons as well or just the apostles?
"These signs will accompany those who have believed: in My name they will cast out demons, they will speak with new tongues; they will pick up serpents, and if they drink any deadly poison, it will not hurt them; they will lay hands on the sick, and they will recover" (Mark 16:17-18).
While Jesus said that signs would accompany believers, he did not state whether it would be all believers or just some believers. Nor did he state how long these signs would be seen.
From Acts we learn, "Now when the apostles in Jerusalem heard that Samaria had received the word of God, they sent them Peter and John, who came down and prayed for them that they might receive the Holy Spirit. For He had not yet fallen upon any of them; they had simply been baptized in the name of the Lord Jesus. Then they began laying their hands on them, and they were receiving the Holy Spirit. Now when Simon saw that the Spirit was bestowed through the laying on of the apostles' hands, he offered them money ..." (Acts 8:14-18). Thus, the Spirit's gifts were distributed by the apostles only and they did not come automatically because someone was baptized.
Jesus once sent out seventy disciples and when they returned, they said, "Lord, even the demons are subject to us in Your name" (Luke 10:17). There were only twelve apostles, so there people who were not apostles who were able to cast out demons. Give Jesus' statement in Mark 16, it would be reasonable to conclude that it continued in the early church. In fact, we see Philip, who was not an apostle, casting out demons (Acts 8:7).