This doesn’t just happen in megachurches but is common in churches of all sizes.
What evangelicals mean by “getting saved” is having a conscious conversion experience and becoming a spiritually born again Christian. It is not making an “internal resolution,” but rather receiving faith in Christ accompanied by a turning from sin.
If this takes place at a church service, the person would be welcomed and invited to become a member of that particular church if they don’t currently attend a church. Many churches have small groups, new members classes, or other discipleship programs oriented to helping new converts grow in their faith.
If someone has truly given their life to Christ (another term for “getting saved”), then they have joined the invisible church already. They are a follower of Christ, not any man. Of course, as a follower of Christ, they would be expected to join a local church for teaching, worship, fellowship, and for pastoral care.
The answer to this would depend on whether you believe in Once Saved Always Saved. I don’t. What I believe is that it is possible to reject Christ through disobedience or unbelief. In such a situation, one could conceivably “get saved” more than once if they backslide and then later return to Christ.
The altar call is used for more than just “invitations to receive Christ.” Not everyone who walks down the aisle is “getting saved.” Many are mature Christians who want to repent of sin or just want prayer for healing or some other issue. Sometimes, people go to the altar to just meet with God.
Just an example of what going to an altar could mean from a Pentecostal perspective:
At the altar we experience: (1) Confession; (2) Change; (3) Consecration/Closeness to God; (4) Communion of the saints; (5) Commissioning into the world.