"Gutten kan ikke vise jenta skilpadda."
Translation:The boy cannot show the girl the turtle.
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Yes it does, and yes you could.
Both of your sentences would mean that he showed the turtle to the girl.
Without a preposition the assumed order is IO - DO, but when you add "til" to the sentence it has to come after the direct object and in front of the indirect object - so the order changes.
Keep in mind that "X til X" is also used to show possession, so in some cases "skilpadda til jenta" can be ambiguous and taken to mean "the girl's turtle".
The declination pattern a noun follows depends on its grammatical gender. For neuter nouns, -a is a definite plural ending, while for feminine nouns it's a definite singular ending.
"en/ei skilpadde" is a feminine nouns, and since all feminine nouns may be treated as if they were masculine, you get two options for the definite singular: "skilpadden" and "skilpadda".