Add skill XP for different activity?

The first question is whether it's possible for something to increase more than one skill at a time. If this is known to be possible, the way we would know that is that either it already happens in game, or someone else has a mod that does it, and then whichever of those things is true, you could look at to see how it is done. I have not personally heard of it being possible, but someone else may have info I don't.

You can. I mentioned it briefly in your other thread, but you'll need to add a loot to all the interactions you want that increases the skill of choice, it would probably be the easiest. Or attempt something similar in this thread (though probably with a different structure, I'm not sure). Right now the interactions are using this to increase the video game skill, but I've never seen multiple skills added to it:
<U n="skill_loot_data">
<V n="level_range" t="enabled">
<U n="enabled">
<T n="lower_bound">1</T>
<T n="upper_bound">4</T>
</U>
</V>
<T n="stat">16712<!--Skill: statistic_Skill_AdultMajor_VideoGaming--></T>
</U>
So adding it as a loot would probably be easiest if you don't want to remove the video game skill increase. Here is one loot example you could attempt (there's different options depending on what you want). I recommend looking at various skill examples and using the TDESC I linked before to build what you want.
<?xml version="1.0" encoding="utf-8"?>
<I c="LootActions" i="action" m="interactions.utils.loot" n="loot_Batuu_Starship_Mission_RR5_Charisma_Skill" s="245051">
<L n="loot_actions">
<V t="statistics">
<V n="statistics" t="statistic_change">
<U n="statistic_change">
<T n="amount">75</T>
<T n="stat">16699<!--statistic_Skill_AdultMajor_Charisma--></T>
</U>
</V>
</V>
</L>
</I>

Is it interaction guitar_singSongs?