you wont get a job in aquatics if you dont know how the cycle works, i suggest you have a read of the beginners section here and absorb as much information as you can. the only acceptable values for ammonia and nitrite are zero and to truely cycle a filter to handle the bioload of the well stocked tank can take anything up to 2 months.
If you tank is truely that size then the video really doesnt do it justice, its very missleading as it makes it look very very small.
If it is the case then i'll withdraw my comments regarding the barbs as i feel it may well be suitable to house them. However, you must also be aware that these guys are very very active fish and although they will probably grow nicely, ( IF you do a good water change every weekend (betweek 30 and 50%) ) you might find that when they reach adulthood they will require more space. So it would be wise for you, even at 16 years old, to save a bit of money and start sweet talking your parents into allowing you a 3 foot tank for around this time next year.
As for adding new stock, it probably wouldnt be wise and Tigers can be nasty little gits and get very fin nippy. I learnt that lesson for myself and had to rehome 17 of them recently.
As for your current water stats, you should consider yourself being in a "fish in cycle", you need to keep ammonia and nitrite below 0.25 at all times and this can only be done with daily water testing and water changes. Do not ever replace the sponge in that filter until its literally falling appart in your hands. if it gets dirty, mucky and gunky, scoop out a pot of water from the tank, take out the sponge and squeeze it in the pot of tank water, then put it back in. In time it will cycle fully an be able to cope with the bio load. Always add dechlorinatior to new water that goes in so it doesnt destroy the bacteria forming on the sponge.
i think i've said enough, good luck with your tank.