Yes, banks do charge a fee for coins deposit.
for example,
http://www.dbs.com/sg/personal/deposit/additionalinfo/priceguide.pdf page 6: over the counter is S$1.50 for every 100 coins or less, and must be sorted to all the same coins, and if is via the coin deposit machine, it's S$0.0075 per piece, and both are irregardless of denomination, as in depositing 10 cent coins incurs the same service charge as depositing $1 coins.
they also noted that the service fee will be waived for children's accounts so at least the kids can still save deposit their coins from their piggy banks.
what my father do, usually after collecting alot of coins from his customers, he changes it with a 7-11 in a petrol station that he often goes. but before that it's understood that you should sort it to the same denomination and perhaps in packets of $10 or $50.
once my dad collected $50 worth of 5 cent coins = 1000 pieces of them... had to change it $10 by $10...
As for Hickey's question on whether the income from busking is taxable, i'm not too sure, but i will think it is taxable, since it is an income afterall.
but singapore's tax rate still reasonable lah, you will only be taxed if your annual income hit $20k.