No, we receive the Holy Spirit when we accept Jesus as our Lord and Savior.

(Ephesians 4:30 NIV) And do not grieve the Holy Spirit of God, with whom you were sealed for the day of redemption.

No, you don't necessarily speak in tongues right after you're saved. That's rare. It happened at Pentecost because there was a purpose for it. I was saved in 1980. I've only seen evidence of tongues once. A singer at church sang a song in Spanish. He said afterwards that he doesn't know the song in Spanish. That it was the work of the Holy Spirit. The vast majority of those who claim they're speaking in tongues are just babbling. It's not a real language. You shouldn't judge someone's salvation based on them speaking in tongues.