I wanted to know one thing, since I don't have any BTC in my wallet. Is it true that the higher the amount of btc the lower the transaction fee and vice-versa?
Not really. Transaction fees are more or less linear to your input size and how much you want to pay for each byte, or in other words the bigger your input (more Bitcoin) the bigger your fees would be. However, you can choose at what price per byte you'd pay for your transaction. Assume that your transaction is 1000 byte, and you choose to pay 1 sat/byte, the fees would be equal with if you send 500 bytes with 2 sat/byte fee. CMIIW.