What happens if I send small amount of btc lesser than fee? I tried to deposit a small amount of btc in localbitcoins.com, but it was smaller than their deposit fee so it was not processed by them, now what will happen to that chunk? and can I get back the btc?
The money has been placed under the control of the recipient.
There is no way to undo a transaction. Even when the recipient declines to perform the service being paid for.
If you overlooked or misunderstood their terms and conditions, they may feel it is for you to bear the costs of rectifying your mistake.
You cannot get back the money directly yourself, but the recipient could choose to make a payment to you of an equivalent amount after deducting the costs your mistake has caused them. It would cost them money in people's time and in transaction fees to do so. For example, no one will want to spend 2 mBTC of their own money just to send 0.1 mBTC back to someone who made a mistake.
Maybe you could ask them whether, if you make a separate payment that itself exceeds their minimum, they will credit your localbitcoins account with the sum of both amounts? Don't be too surprised if they decline.
Alternatively, perhaps you could consider it a donation to a good cause?