Q: Is speaking in tongues available to all believers?

A: Yes. In Matt 3:11 Jesus told the Pharisees and Sadducees after John had baptized Him in the Jordon, "I indeed baptize you with water unto repentance; but he that cometh after me is mightier than I, whose shoes I am not worthy to bear; he shall baptize you with the Holy Ghost, and with fire.

In John 14:16-17 Jesus told his disciples, "And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever. Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him; but ye know him; for he dwelleth with you, and shall be in you."

And again He tells them in Mark16:17 And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues.

Acts 2:38-39 Then Peter said unto them repent and be baptized every one of you in the name of Jesus Christ for the remission of sins. And ye shall receive the gift of the Holy Ghost. For this promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
If you're a believer (born again) then speaking in tongues is available to you.

Again in Acts 2:4 And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.
This verse clearly states that they were all filled, not some or a few, but all were filled. All means all.