Okie dokies.
Here is a link to our
Beginners Resource Centre
And here is a few specific links you need to read...
What is cycling - This explains all about what the word/process means.
The Nitrogen Cycle - Explains the things that are being 'cycled'
Fish-in Cycling - This is the situation that you were put in due to bad advice from the pet shop you bought your fish/tank from. It exposes the fish to toxins which shortens their lifespan considerably. And with sensitive fish like neons it often kills them within days. The reason the last 3 are surviving better is because they will have been subjected to much less toxins...you will understand why after you have read all of the info on cycling.
Anyhoo....
60l isn't big enough for sharks, sorry

I really can't stress how much they need re-homing.
Betta fish - Aren't normally good in community tanks, you may have been lucky here if you haven't seen any aggression so far from him. However always be aware that fish like neons can get nippy. Again you may have absolutely no problems, just be aware of it.

Neons - I wouldn't expect the neons to last as long as they should. Not too be all doom and gloom...but chances are when you added the 2 sharks and 3 neons this will have caused enough of an ammonia and nitrite spike to cause some damage. So although they weren't exposed to anywhere near as much as the first 7 (and are therefore still alive), I would be surprised if they last much longer than 6months.
If anything is unclear or you have any questions. Please just ask.
Everyone will do their best to help.