Hello and welcome.
First off you are not the only one to make the mistake of adding fish too quickly, including my self. As Erk mentioned you first need to concentrate on cycling your tank. A fish less cycle is best, easier on the fish and on you (less water changes). Ideally you should return all the fish you have currently and start on a fish less cycle, if that is not possible, then prepare yourself for a lot of hard work testing and changing water. Erk gave you the links for a fish in cycle (where you are right now) and the link for fish less cycling. Here is the link for the Beginners Resource Centre: http

/www.fishforums.net/index.php?/topic/277264-beginners-resource-center/. It has a ton of great information read through it. Also there is a link in there for people willing to donate mature filter media that will help you out a lot. Now for your other issues:
Get a good liquid test kit. I, and many people here, use API but Hagen Nutrafin and Saliferts are also quite popular. If you are in the US you will probably find it easier to locate API kits, if in Canada Hagen Nutrafin is the standard at the stores, in UK Hagen Nutrafin or Saliferts can be easily had. If you can't find any of these in you LFS (local fish shop) then you can order any of them on line. You want to get ammonia, nitrite, nitrate and pH (Hagen and API have a kit that contains all of these, salifert is individual tests only) Check out this post, not a perfect article but might help you out with tests: http

/www.fishforums.net/index.php?/topic/315183-liquid-test-kits-how-to-perform-and-read-tests/page__p__2611010__fromsearch__1&#entry2611010.
Next, if at all possible see if you can exchange your under gravel filter for an external or a HOB (hang on back) filter, or even an internal filter. Gravel filters are a bit of a pain to maintain. Dirt will inevitably get trapped under the filter grate and you will have to take your entire tank apart to clean it. You can get a decent HOP filter for not very much money. I have an Aquaclear 20 on my 5 US gallon tank (roughly 20 L). The AC20 will accommodate a tank up to 20 US gallons and the cost is around $25 US. Not sure of the price in the UK but I am sure it wouldn't be that much more. Also the AC filters are really easy to add/change your filter media around to meet your specifications. If you choose the AC (or similar HOB filter) you can remove the carbon pack to make room for some extra sponges, or additional BioMax (AC brand, but can use anything rated for BIO filtration), or your donated filter media. That will give you extra surface area to grow bacteria.
Finally, get some water conditioner and a heater. The heater you already said you will get one, I think a 25watt should do you fine, but double check that with what the heater says (it should have on the box somewhere what size tank it is for). As for water conditioner you really need that. If your water company only uses chlorine to treat the water then you can let your water sit for 24-48 hours and the chlorine will evaporate out, but if they use chlorimmine (and a lot do) then that can only be removed with a dechlorinator. Prime is what is generally used here, a little more expensive to buy initially, but it is very concentrated so you don't have to use a much of it, so in the long run it is cheaper.
As for feeding your fish, I am not familiar with eels so I will leave that to someone who knows.
Good Luck