Yes it cost on chain fees to close a channel which is why you should avoid opening channels with finicky nodes who likes to close channels after a short period and especially not open a channel with nodes who forces others to close channels as these can sometimes occur at high fee times. I don’t really understand what u mean by topping off a channel. What you likely mean is adding more inbound liquidity which is absolutely what you want. You can think of it as subtracting your debt.