Expression to replace characters in Attribute table

Use this expression:

array_to_string(
    array_foreach(
        string_to_array( LineCodes, ',' ),
        if(
            left( @element, 1 ) = '-',
            substr( @element, 2 ) + 'B',
            @element + 'F'
        )
    )
)

string_to_array: splits string into an array using comma
array_foreach: runs given expression for every element in array
array_to_string:concatenates elements into a string separated by comma

You can define your own custom expression function in Python and then use it in field calculator.

@qgsfunction(args='auto', group='Custom', usesGeometry=False)
def custom(input, feature, parent):
    if input is None:
        return None
    numbers = [int(num) for num in input.split(',')]
    def f(num):
        if num > 0:
            return '{}F'.format(num)
        return '{}B'.format(abs(num))
    result = map(f, numbers)
    return ','.join(result)

1. Define it by running the code above as a script in Python console:

2. Use it in the field calculator:

You may also try the following expression

array_to_string(
    array_foreach(string_to_array("test"), if(to_int(@element)>0, @element||'F', abs(@element)||'B')
    )
)

See, for example below

P.S. IMHO using the regexp_replace() is pointless because more changes have to be applied rather than substitutions.