Betta in 2gallon tank, want to add filter

Question
Hello... i just bought my first fish yesterday, a beautiful male Betta. After fighting with the guy that YES i DID want a 2 Gallon tank for a "little" Betta instead of a smaller one. (I wish i had room for a 5gallon actually) I left with; 2 gallon tank, a small heater & themometer (seems to keep the tank at a steady 78 degress) some silk plants, gravel & 1 decoration and a bag if there pre-cycled water from one of there tanks holding just live plants.

I did not buy a filter yesterday as i was told they dont like current and could get sucked in by many of the staff at the store, but upon getting him home and in his tank i did some research and so many people with Betta's were saying you should have a filter.

I found a sponge filter (Elite Mini Underwater filter good for tanks UP TO 3gallons) with a valve to controle the flow, so went out and just bought it. I put the filter in the tankand put it at it's lowest setting.

My Betta seems to not be having too much trouble with the flow from the filter unless he gets closer to it. (he can swim easily on the opposite side of the tank, but has to swim harder in the open area - no silk plants - on the side with the filter)

So here are my questions;

1)should i have put the filter in? i didnt have the tank cycle as i have never had a fish tank before and never researched about it as i was told not to get a filter, so there for wouldnt need to.
2)the Betta is in the tank already, (and i dont have anywere else to put him while the tank cycles) so if i leave it in will he get sick (i was told that putting a filter in the tank uncycled will cause ammonia spikes and stuff)
3)should i just take the filter out all together? if i do how often should i clean his tank?

He still isnt eating as i assume he is still traumatized from his move yesterday :( so i dont want to stress him out anymore then i need to.

thanks in advance Megs >.<

Answer
Megs,
yes, the filter is a good idea.
don;t worry about the cycle too much with the beta as if the levels get too high they can extract 02 from the air.
you should clean the tank when dirty, you will be able to tell, also you will want to change a pint of water once a week to keep things fresh.
I believe all you need to do now is enjoy the fish...don;t overfeed.
If  you have further questions, just ask.