With Trust Wallet, you can send your funds anywhere they are supported. In principle, a small fee will always be required in one form or another before you can make transactions. Sending and making trades will all require fees in order to be processed. Trust Wallet does not charge any fees, this is mandated by the blockchain or the network where a token resides. This is explained further in this article: Cryptocurrency Network Fees.
Always check the compatibility with the currency you are trying to send. Sending crypto is irreversible and your funds may get lost.
Tokens that require fees
Almost all of the major coins and tokens that is supported by Trust Wallet will have a certain fee deducted in order to process a transaction. Fees are not collected by your wallet, but it is given to the miners.
Here is a list of tokens that will require fees:
Ethereum ERC20 tokens
ERC20 tokens require some ETH in order to make transactions.
Binance BEP2 Tokens
BEP2 tokens require some BNB in order to make transactions.
TRON TRC10 and TRC20 Tokens
TRC10 and TRC20 tokens require some TRX in order to make transactions.
Other Blockchains With Fees
There are some blockchains that have a dual-token system. These chains generate a secondary token while you are holding them on your wallet. The secondary tokens serve as fees on their respective chain to process transactions.
Here are the blockchains that has a dual-token system:
Ontology (ONT) and Ontology Gas (ONG)
ONG is required in order to process transactions in the Ontology Network.
Vechain (VET) and VeThor (VTHO)
VTHO is required in order to process transactions in the Vechain Network.
Theta (THETA) and Theta Fuel (TFUEL)
TFUEL is required in order to process transactions in the Theta Network.