JackOfAllShades. I recognize you're new to the community and to the hobby-- welcome to both, and I'm sorry you're having a bad experience with the hobby.
Here is something that might be hard to hear, but I think I have to say it up front: through no fault of your own you might not be able to get what you need or want. There really isn't a proven way to make people stop acting like this. But there are some strategies that might help, or might get you to a point where you know this isn't going to work.
Several things leap out at me from the description of your problem:
1) Q's player "doesn't want to play the game."
2) Q the character resists or rejects plot.
3) Q (and Q's player?) have pronounced anti-social and bullying tendencies.
4) Ajax follows Q, as far as causing trouble goes.
I'm not sure if 1) and 2) are meant to be the same thing or not. Specifically, I'm not sure if "doesn't want to play the game," is meant in a literal fashion-- the player wants to do something else with their time, resents the activity and may be sabotaging it-- or is just another way of saying the they reject the plot.
If it's literal, this is a huge problem and I don't think it's solvable. You can't make someone enjoy something they don't enjoy.
If it's not literal, it might be a clash of play styles-- GMs and players fall at different points on the spectrum between wanting plots directed by the GM (which is what you seem to want) vs wanting plots directed by the players. At the best of times, these different play styles don't mesh very well if the players and/or GM have widely varying preferences. This is where something like a Session Zero can be very helpful.
But be mindful that both these position can get pathological. GMs who prefer too much of a GM-directed plot end up railroading, and players who reject plot too much end up causing chaos very much like what you describe.
3) is another red flag for me. It is not something I will tolerate in my games as a GM, and as a player it becomes a he-goes-or-I-go situation if it does not resolve quickly. There are a lot of justifications for this sort of behavior ("That's just what my guy would do!" "That's just how that player has fun!") but they all ring hollow to me after a point, because in the end it is domineering, bullying behavior by proxy.
No one's role at the table should be to provide a target for the emotional outbursts of another player or character. Sure, some times there will be moments of real story telling drama when two PCs find themselves on opposite sides of an important issue, but petty thievery, fight-picking and vandalism are not covered under that aegis.
4) makes it sound like Q/Q's player is the real focus. If not, they are probably the larger of the two problems, and solving that might cause the other problem to resolve on its own.
So with that said, what I would probably do is this:
First, talk to your GM privately. It sounds like you are on the same page, but it helps to be certain, when you are trying to provide a unified front. If there's a fifth non-problem player (you description makes it sound like this game is you plus four others) you should probably see where that person is, too.
Then, have something like a Session 0, as linked above... although it would be a retro-active one. And you will have several issues to cover.
One of them is somewhat open-ended: How do we get to a game we all want to play in, on that spectrum of plot-driven vs open-ended? This is the one I would probably lead with, since (unless the GM or a player is hard core to the point of dysfunction) there are many valid view points, and therefore there is room for constructive criticism and compromise.
The other, for me, would be non-negotiable: No more anti-social or bullying behavior directed at other PCs, and preferably not at NPCs without reason. It's just not fun. It's not fun to be the target, and it's not fun as a PC to be cleaning up after the results when NPCs are the target. I am thinking that a reasonable compromise on the first issue will make a harsher stance on this problem - unhealthy behavior - easier to swallow.
But here's the thing: as much as I wish I had a silver bullet to make people stop doing things like this, I don't. No one does. And if nothing works, only you can decide if the game is still worth your time.
Best Answer
You don’t give us a criterion for “should”
If your criterion is damage potential - maybe. The long bow has a higher average damage on a hit than a Fire Bolt (6.5 vs 5.5). However, if her Intelligence bonus is better than her Dexterity bonus then the bow will miss more often. Where the crossover point on damage output is depends on the difference in the bonus and the AC of the target.
If your criterion is looking like a bad-ass wizard shooting fire from your fingers, then no.
If your criterion is looking like a bad-ass elf sniping foes with her ancestral weapon, then yes.