Probably the same princesses from the same realm can use their specific ones, along with the ones that every princess can use. However, special spells (like Lyna's Crystal Levitus) cannot be used by other princesses, except the Borealian ones.
188.8.131.52 wrote: But how do you know if a spell can be used by more persons?
I know that IrisIsBestPrincess beaten me to the punch, but I might as well put my analysis for this question anyways.
Yes, it is possible that they can use spells that Talia or any other Crystal Magic users have used. Anyone who knows how to use crystal magic could use and learn any known crystal spells that exist.
However, through my careful observation of their battles against the twins and Gramorr in Season One, the question that you should be asking yourself is, “Would they want to use it?”. Not all the princesses have an all-rounded skillset to use all of the spells known in the LoliRock universe. Whether or not the spell can be used by multiple people depends if the requirements are met. By requirements, I talking about three conditions that I hypothesize in order to answer the question.
Before going any further, keep this question in mind: “Can they use the __________ spell?” (The blank representing the spell you want to insert.) After that, it brings up the three conditions that are attached to it.
Here are those conditions: 1) Were they taught on how to use it? 2) Is this spell practical for each individual to use in daily combat?, and 3) Would they want to add that spell in their repertoire of spells they specialized on?
Conditions and Analysis:
1) Were they taught on how to use it? (Yes or No)
In LoliRock, most of the existing crystal spells are taught by a practitioner of those spell.
It would not be possible for someone to master a spell that they seen or heard once without knowing the fundamental concept of how the spell works without someone teaching them. For example, if someone were to bake a cake for the first time, would the result be perfect as the one in the recipe? No, not at all because of the lack of experience on baking a cake. Hence, the cake would not look and or taste as good on the first try. By understanding how a spell works and practice using it, the princesses can produce the result they imagine it to be when they use it. 
Without anyone to teach them the spell, it would be difficult for them to utilize it in the first place. Almost like building a house without instructions.
2) Is this spell practical for each individual to use in daily combat? (Yes or No)
In order for a Crystal Magic user to use a spell that someone else used, they must be able to cast it without problem or else it would be pointless to use the spell in the first place.
For example, Truncolus, a spell given to the twins, by Gramorr, is used to annihilate the princess. It requires two magic users to cast it because it is a powerful spell, with the exception of Gramorr. However, the spell was not practical for the twins because they could not synchronize with each other during the time they cast it. (Xeris)
Gramorr: “Was it not powerful enough?”
Praxina: “Yes, it was. But, as you know, it was a two-person spell. And a chain is really only as strong as its weakest link.”
Praxina suggested that Mephisto isn’t strong, in her opinion, despite Truncolus being a powerful spell and therefore would not use the spell again. Her problem being Mephisto getting in the way of casting it. Same concept applies for the princesses, too, in the future on whether or not the spell is practical for them to use.
3) Would they want to add that spell in their repertoire of spells they specialized on? (Yes or No)
Not all princesses will uses the crystal magic the same way. If you noticed, each princesses has a specific style of spells that they mainly/prefer to use:
Team LoliRock stated that Jean-Louis Vandestoc references the princesses as chess pieces in a philosophical concept. Each princesses have unique skills and personality that makes them different from each other, same with chess. Because of this, whether or not a princess would use that spell is up to them to decide based on their preference of magic. This concept can also be applied for “Team Gramorr”.
If these three conditions are met, then yes, the princesses are able to use that one spell as the other princesses. But remember, just because one spell met those conditions does not mean that the same is said for the other spells. Therefore, you have to repeat this process with the other spells to see if they can possibly learn it under those conditions.
Just so you know, you do not have to agree with most of the stuff that I've said since these are just my personal observations and not words/ideas/concepts explained by Team LoliRock or any of the LoliRock staffs. I'm just giving a thorough conceptual explanation of how I think anyone can use crystal spells if these specific requirements are met.
And one question that I have is, “What is ‘soap’?” I’ve seen you use that term twice and I do not know what it means, so could you explain what it mean?. (I know it is not the cleaning soap. Lolz.)