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Suppose some GPS receiver getting information ("connected") from 4 satellites, and from some reason disconnected from one of the satellites, and instead connecting to new one, so in total still there are 4 satellites as sources for information.

Is this possible? And if so, does some accuracy error (UERE) occur?

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No, if you watch your GPS you will see satellites come in an our of view all the time, and with WAAS you actually have some satellites that are not in your view being used for correction. The base station you diff correct to likely has the old/new satellite info also helping with the correction.

AS for using 3 vs 4, 3 will give you the horizontal location the 4th helps with altitude (Z / 3D). However the more you are using the better the math for the location.

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