Hi lowkey, welcome to the forum

Don't worry, we can help you with your new tank. And there's no such thing as a stupid question

To tackle your list of questions first:
1. Filter. You don't need carbon, it's a hangover from the very old days. And you don't need the algaway pad either. The simplest would be to buy a filter sponge, any make as long as it's a bit bigger than the carbon cartridge and alagaway pad combined, then just cut it to the same size as those two. It is better to have a tight fit than a bit loose so that the water can't sneak round the edges.
2. Once the tank is cycled and fully stocked, change about 50% of the water every week. Until then, you need to test the water every day for both ammonia and nitrite and do a water change whenever you see either of them above zero.
Unless you have live plants growing in the gravel, clean that at every water change. Use a siphon tube made for fish tanks. These comprise a length of flexible tubing attached to a rigid plastic cylinder. All you do is push the cylinder down into the gravel and watch the muck flow up the tubing. When the water is clear, move on to the next bit of gravel.
If you have live plants in the gravel, do this only in gravel where there are no roots.
3. If you change the media to sponge, it needs changing when it falls apart or loses shape. Sponge will last for several years. When it gets covered in brown goo, squeeze it in water you take out during a water change.
Carbon gets full and needs replacing every few weeks - but you throw away all the bacteria on the carbon and outer stuff of the cartridge. Carbon is only useful for removing the brown colour that leaches out of wood, and for removing medication after treatment has finished so you don't need it full time.
The filter description says it contains biomedia, mechanical floss, carbon and algaway pad. What exactly does the biomedia and mechanical floss look like? If the floss is a layer of something that looks like pillow stuffing, you do need to replace that because it clogs easily and won't wash without going into holes. It is not a very good home for the bacteria so it doesn't matter if it is changed regularly.
And depending on exactly what the biomedia is, that will need changing every few years.
4. To be brutally honest with you, danios are not suitable for this tank. They may be small but they are such fast swimmers they need a tank at least 100 cm long. Their temperature range is 18 to 25 deg C so they are best kept at around 20 to 22 C.
Zebra danios If you can bear to part with them, there are fish more suited to this tank.
5. Stocking. This is more complex than most people realise.
There are several things to take into account. The starting point is the hardness of your tap water. I know you have test strips but they can be inaccurate so I would also look on your water company's website. That should give the hardness, somewhere. Assuming you are in the UK, it is most likely to give your hardness as mg/l calcium, with maybe a button to convert it to other units. See what you can find, and post both the number and the units on here. If they give it in german degrees and/or mg/l calcium carbonate, those are the two used in fish keeping; for any other unit we can convert them to those two.
The next thing is to look at the recommended tank size for any species, and the best site for that is
http://www.seriouslyfish.com/knowledge-base/Then look at the temperature requirements on the same site.
Finally, having drawn up a shortlist of fish that all need the same conditions, look at their behaviour. For example, your danios are very active, fast swimming fish. They would badly stress fish like honey gouramis which are placid sedate fish.
Once we know your hardness, we can take it from there.
6 Algae. Yes you can have fish or shrimps - though the tank is too small for most algae eating fish - but no creature will eat all types of algae. It is the responsibility of the fish keeper to keep algae under control. There is always some algae in every tank, it is only when it gets out of control that it is bad.
Algae are plants so they need three things - light, carbon dioxide and fertiliser. They need to be in balance to keep the algae under control. Not enough of one, or too much of one will make the algae take over. The usual culprit is having the light on too long.
7. Lights.
Fish need the same pattern of lights every day, so they are best run on a timer. If there are no live plants, 6 hours is the maximum I'd have them on for. Set the timer so they are on when you and your children are at home to see the tank. if you do have live plants you need to experiment to find the duration that lets your plants grow well without growing too much algae.
Blue light encourages algae. I would stick to just white light if your lighting allows that.
8. Background. Whichever you prefer

The general consensus seems to be that a black background makes the tank look better.
Now that I've dealt with your list -
You need to be able to test for ammonia and nitrite. Most strips do not include an ammonia test (it because it needs a different length of time to develop) so you'll have to get a separate tester for that. And yes, liquid reagent testers are generally regarded as being more accurate than strips.
There is a How To sticky on fish-in cycling in the Filtration & Cycling section; I suggest you read that if you haven't already done so.
Tetra Safe Start is one of the two recommended bottled bacteria products so you may be lucky and find it does work (it's when it's been allowed to get too hot or too cold anywhere on its journey to your tank that it doesn't work)
As I mentioned earlier, think seriously about keeping the danios. Their temperature requirements will serious limit the other fish you can keep, and they really do need a bigger tank.
Do you have any live plants in the tank? They help keep the water good, and fish like them. After many years of not being able to keep plants alive, I am now a convert to planted tanks. But not those that you see on-line. Mine tank is full of slow growing, easy plants attached to wood

Sorry for the essay.......