So many questions in one post!
As an ex EFL teacher, I'll try to answer a few.
The use of the present simple tense in the if-clause does represent her ability to remember in the future, especially as you have included the word 'then', which refers to a time in the future ('next month', in this example).
'Will' can be used in the if-clause to indicate volition, not futurity.
e.g. If he won't follow the rules, he will be asked to leave.
The 'won't' here means 'refuses to' (and could be replaced by 'doesn't', but without the idea of refusal); the 'will' refers to the future.
e.g. If he will not share the housework, we will give him his notice.
Here the 'will' indicates a refusal to, or an insistence on not sharing the housework (and could be replaced by 'doesn't'); the 'will' refers to the future.
'Will have' refers to a completed action in the future, and is not appropriate in the sentences you quote here.
'If it will rain tomorrow, I must take an umbrella', is grammatically incorrect, and should be 'If it rains tomorrow, I will/must take an umbrella.' The weather cannot have volition, as in the above examples.
Hope this is of some help!
Student or Learner