Keeping a clean tank

Question
About a month ago, I purchased a 10 gallon tank and 9 tetras on a total whim. I really should have done my homework, but what's done is done. I hadn't realized all of the complexities of keeping a healthy tank and I feel pretty silly now, but I'm very eager to learn about how to keep my fish healthy and happy. I have 2 black skirt tetras, 3 serpae tetras and 4 tetras that have been dyed pink and blue (They look like a sort of skirt tetra, I didn't realize they were dyed when I bought them). Miraculously, all my fish have survived this first month, despite my incompetence...
I don't have any live plants in my tank. I do a 15-20% water change once a week and, I feed my fish a small amount once a day. The only issue I've had is algae growing on my gravel, decorations and walls. I sorted that out by rinsing the objects in clear water and wiping the algae off the side of the tank. I also realized I was feeding them too much, so I cut down on how much I fed them.
What I am wondering is how to clean the gravel. I would also like to know what sort of gravel cleaning device would work best for me in terms of my small tank.
I would also like to clarify how often to change a filter cartridge. The instructions say every 2-4 weeks (which I think is a pretty big time gap to choose from) yet something I read said to rarely change it and just rinse it in aquarium water to keep the bacteria alive. I don't know if that applied to my type of filter ( a Regent brand filter, I couldn't find a picture).
Any help or advice regarding keeping my little tank healthy is appreciated! =)

Thanks!  

Answer
Hi Kathryn
It's common for algae to grow in newly set up tanks.  What color is it?  Sounds like what you've done so far is right on.  
For cleaning the gravel and doing water changes, the best thing to get is a small gravel vacuum.  The only way I can describe the size is to take your thumb and first finger and make a circle.  That's about the size of the "tube" on the gravel vacuum that you want for your tank size.  Anything larger, and it sucks the water out too quickly and you don't have much of a chance to clean the gravel well.  I use that type of gravel vac in my 10 gallons, and even managed to use it in a 5 gallon tank before.  Walmart carries these fairly cheap as well. You'll also need 2 or 3 buckets, and label the outside of them FISH so they don't get used for cleaning other stuff.  It'll clean the gunk out of the gravel and remove water at the same time, so that's the best way to do the water changes.

For the filter cartridges, I just posted to someone on the same thing :)  You can get away with just rinsing it off in a bucket of tank water, just scrub the blue part off with your hand.  Usually doing that monthly is sufficient, but if appears to clog or get dirty, may have to do it a little more then that.  And then usually about 3 months or so they need changing out completely.  What I do, I got tired of spending all the money on those filter pads, they are expensive, I just buy a bag of filter floss from the pet store, costs a few dollars, I rip off a big chunk and stuff that in the filter and use that instead.  But with your filter type, yes that would apply-the just rinsing it off.  I believe those come with the complete tank set ups from Walmart right?  I think I have one or two of those filters.  The filter pads are blue, on a black piece of plastic with carbon inside them right?  So that should be fine to do.  

If you don't have one, I'd also recommend picking up a test kit that tests ph, ammonia, nitrite, and nitrates.  The liquid dropper test kits are better/more accurate then the dipsticks.  I'm guessing you've probably figured out or read about the cycle process by now?  If not, here's a link to read over, it's the first article on there:

http://freshaquarium.about.com/od/startupcycle/Step_5_The_Cycle.htm

Everything you're doing now, sounds great.  The only suggestion I have, get the water test kit, and test your water.  If you still have ammonia or nitrites present in your tank, you should up your water changes to daily to help dilute those toxins in the water.  Then, once your tank cycles(ammonia and nitrites at 0 ppm, and some nitrates showing), you can go on the weekly 20%.  

Another thing, not sure what you're feeding the fish, but just about all fish will benefit from a varied diet.  A good pellet or flake food should be the main staple, but during the week switch it up a few times with some frozen or freeze dried blood worms, frozen brine shrimp, spirulina flakes or veggie crisps.  It just helps to keep them healthy.  And all frozen foods should first be thawed in a bowl with some tank water before feeding.

Think that's it, good luck with your new tank, and hats off to ya for doing research on it :)  And don't feel bad, I think most of us have started out that way-on a whim, not realizing all that's involved with it, I know I did :)  Let me know if you have more questions.

Christy