I’m having trouble understanding the meaning of disposal advance. What do the following sentences mean?
These are the amounts that we believe you are entitled to. You can derive no rights. The amounts are at your disposal advance.
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Without more context it's impossible to say, but it sounds like a message from a bank worker who doesn't speak good English.
Disposal is sometimes used by banks to refer to money you have available to you; a current account is sometimes called a disposal account.
Advance may be a typo for advice, a word used by banks not for tips and suggestions but for telling you your account balance.
So perhaps disposal advance is a typo when they mean to tell you what your current account balance is.
Alternatively, there may be a missing "in":
At you disposal means "available to you" and in advance means before time, before the usual time. This might fit with You can derive no rights, which is a disclaimer saying that you can't have any extra rights even with the offer they're making.
However, You can derive no rights doesn't sound like natural English either and may be a literal translation. My guess is from Dutch, as it turns up on many .nl websites.