Are your prices fair? Based on the market, quite possibly. Based on your talent? No. You could charge more.
In my experience (I'm an ex-photographer turned translator), freelance business is about building good relationships with clients. Low prices only brings in people looking for bargains, and some of them might harass you to lower your price further before delivery, using sudden "budget problems" and the like. And the moment you raise your prices (even if it's just to keep up with the Costs of living index), they look elsewhere for lower prices. The idea is to charge a decent price and give the best service possible. Your client(s) must feel that you’re there to help him/her/them their project a success. To do that, just ask the questions that help you understand what your clients want, keep them updated on the progress of your work and accept, to a certain extend, to go back and modify the art to meet their expectations.
For instance, instead of charging $40 for a character design, charge $70, but allow your client to make one important or three minor modifications along the way, instead of just a minor one. (Doing so requires the use of a software with layers tool like Gimp, Photoshop, etc., of course.) Now, instead of selling art to your client, you actually rent your services as an artist instead. Product business is more dependent on the product, and its availability on the market. Service business is more dependent on the relationship between the client and the service provider.
You'll probably get less clients at first, but your business will likely grow more solid over time, as your clients will turn to you not only for your great art (and there are a bazillion of artists selling art out there), but also for your great business practices. As your business gets more solid, think of increasing your prices at least every year to reflect the change in the costs of living. If you wait 10 years with an average inflation of 2% per year before adjusting your prices, you could have to suddenly raise your prices by 10 to 20% to keep meeting ends. Not great news for your clients.
Of course, the price an artist can charge also depends on how good (or not) he/she is. Some bad artists charge way too much for rather poor work, some excellent artists can't make a living because they don't charge enough for their near-masterpiece creations.
A good way to set your price properly is to compare yourself to other artists who produce work you believe is comparable to yours, in terms of quality and orignality. That's a very subjective exercise, but it is a very efficient way to get a rough idea of how much you should charge. Compare with multiple artists to get a good idea of how much you should charge: comparing with only one may be a bad idea if that artist is actually overpriced or underpriced compared to the market.
If you want to be paid by the piece, I suggest you sell backgrounds separately from characters. For the game designer, this can result in good savings, and for you, as an artist, it allows you build a solid price list. (Please take note: all the financial figures that follow are fictional, and only used for explanation purposes.)
Getting $100 for a character with background might be nice, but afterwards, if the producers suddenly change their mind and want 4 additional characters instead of the original 3, their art budget has gone from $300 to $700. Charging $60 for each character and $40 for each background (which is about the same price and work time as $100 for a character with background if you use the proper software) means the game designer can pay $460 (7 characters times $60, plus $40 for the background) instead of $700 for the same work. If the same producers want 20 backgrounds and 10 characters, it will mean $1,400 for you ($800 for the backgrounds plus $600 for the characters), which isn’t bad, but it will also be good for the game designer, who will have to pay $1,400 instead of $2,000 (20 times 10 characters with background at $100 a piece).
Some artist resort to "bulk prices" strategies. Using the numbers above, let’s say you subtract $10 for each additional character, down to a minimum of $30 per character. For the designer, it means paying $130 instead of $140 for two characters, $180 instead of $210 for three, etc. For the artist, it means having a better chance at getting more work. Be careful not to charge too little by giving too big rebates, however. Having to draw 28 characters at $30 can look interesting in financial terms, but it’s not worth it if you put 10 hours drawing each character.
As part of a "bulk prices" policy, you can also add in a certain amount of "variants" for each character—smiling, frowning, etc.—so your client can get a multitude of facial expressions that make the characters look more alive, more interesting (a must, nowadays). Such bulk pricing can be charging a fixed amount of $10 for 5 additional facial expressions, or charging $3 for each additional expression regardless of the amount of the said expressions.
All this depends on your pricing policy. This part is very different from one artist to another, and you need to adjust yours according to how you want to do business. Avoid too complex pricing policies, however: they just scare clients away.
Some artist ask for royalties. Say, 5% or 10, or 12% of the game worldwide sales, paid on a quarterly or yearly basis. For the artist, it means waiting longer before being paid. If the game is a huge success, it also means the earnings might be better than if the artist had opted for a pay-by-the-piece pricing policy. However, it can turn out real bad if the game is a huge fail.
For the game designer, it means not having to worry about such expenses while creating the game. Designing and releasing a game requires a lot of investments. From writing to programming, to marketing, etc., everything costs something. Saving $1,200 in artwork means this money can be used elsewhere, and that the . Usually, only visual artists and writers go for the royalties. Sometimes, in the case of small, independent games, a game programmer will partner with an artist (and a writer, too), sharing the expenses, the free time spend making the game, in exchange for sharing the profits accordingly. If the game fails, all partners have worked for nothing (or next to nothing). If the game is a success, all partners will benefit, not only financially, but also in gaining much welcome visibility. The only backdraw is when one of the business partners is not pulling his/her weight, in which case the only solution is to kick him/her out. So make sure you pull your weight and that you partner with people you can trust.
In either case (royalties or business partner), it requires a solid contract, one which needs to be checked by a lawyer or another expert. This is a necessity, which is usually paid by the producer(s) of the game. As an artist, don’t ever agree to pay for the legal fees of a royalty agreement, or at least, do not pay more than what you will earn in royalties afterwards. For associate agreements, only pay a share of the legal fees that equals to the share of the profits you will get. If you get %40 of the profits, you shouldn't pay more than %40 of the expenses, and that includes legal fees surrounding business agreements. One last word of advice: if you strike a deal with a game designer working in a different country (either for royalties or partnership), make sure you have access to legal resources in case something goes wrong. Having to sue a game producer living in a foreign country for unpaid royalties can be very difficult if that producer has closed his/her business and reopened it under a new name. Make sure your agreement includes provisions in case this happens, check to see which laws from which country apply to your royalties/partnership agreement, and avoid dealing with people who have their business place in countries known for their scams rather than their thriving business (yes, I’m talking to you, Nigeria).
So, are you charging too much or not? I my opinion, you could charge more, provided it comes with the kind of services I mentioned above (such as working hand-in-hand with the game designer, making design adjustments along the way, etc.). A work sold $120 only earns you $6 an hour if it took 20 hours to complete. In Canada, where I live, it's below the minimum wage (by almost $5). But in developed countries, such earnings might be good. And to help pay the bills as a studend, it's quite decent, especially if you love making art.
Great art, by the way.