What happens if a runner tries to score a double then goes back to his first scored base?

Question

What happens in the following case:

1. A batter hits the ball and it touches the ground.
2. They run and touch first base.
3. Thinking the ball is far enough, they begin advancing to second base.
4. However they realise they cannot reach second base.

Can they retreat to first base and occupy it? Or can the defending team tag the unoccupied first base for an out?

The same question in another way: what if the batter ran very quickly and slides to reach the first base then after safely touching it kept sliding away from it (without intention to advance but he was just sliding too fast). Is it still his base?

Answer 1

Once the batter reaches first base, the "force" is removed. The batter can advance at their peril, but must now be tagged while not touching a base to be put out. Tagging a base alone is not sufficient.

The same question in another way: what if the batter ran very quickly and slides to reach the first base then after safely touching it kept sliding away from it (without intention to advance but he was just sliding too fast). Is it still his base?

This is not the same question. The difference here is that there is no attempt to move toward second base. First base is special in that it can be overrun without penalty.

MLB Rule 5.09(b) lists ways that runners will be called out. 5.09(b)(4) states a runner is out if:

(4)  He is tagged, when the ball is alive, while off his base.

EXCEPTION: A batter-runner cannot be tagged out after overrunning or oversliding first base if he returns immediately to the base;

In your first scenario (3) removes the "returns immediately to the base" part and places the runner in jeopardy.