If you only have a 10 gallon tank, I wouldn't have more than 1 school of 5-7 fish. Tetras love lots of room to swim. Since tetras don't do well in a new tank, fishless cycling would be recommended for you. I have a link below on how to do it. All cycling does take 4-6 weeks. Bio spira supposedly is another alternative to helping the cylcing process, but I haven't used it yet.

I wouldn't feed my cichlids tetras. Most places recommend only feeding live brine shrimp.
Fishless cycling

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Phishie

"An ounce of prevention is worth a pound of cure."