There are two types of sentences that can be completed using so.
- When you want to say that you did something for a specific purpose or intent you use so that. For example:
I went to Fiji for my holidays because I wanted to relax and get a tan.
In this case we would use so that to show purpose or intention , i.e.,
I went to Fiji for my holidays so that I could relax and get a tan.
NOTE: This only tells us the purpose for going on the holiday, it does not tell us if the purpose was realised.
- When you want to say that something you did was simply the effect of something else that also happened you use so.
It rained all day. I had nothing better to do and read a book.
In this case we use so to show that my reading a book was an effect of the fact that it rained, but the rain was not produced on purpose to make me read a book.
It rained all day, so having nothing better to do, I read a book.
NOTE: This tells us the fact that it rained all day had the effect that I read a book. So, the rain caused the effect that I read a book, but it was not a purposeful or intentional effect.
To complicate matters, the 'that' in 'so that' can usually be omitted from the sentence. This leaves two different types of sentence which both use so.
The first type of sentence (i.e. purposeful) can use either so or
so that interchangeably.
The second type of sentence (i.e. cause and effect without intent) can
only use so, you must not use so that with this type of sentence.
Returning to your questions.
Your first sentence is clearly of the first type. The purpose for the person to let you know that they are about to send the item is so that you will send them the payment. This is not simple cause and effect without a purpose, there is implied intent to the first action.
Your second sentence is more difficult to answer as it is ambiguous. The two meanings can be expressed as follows:
(a) I deliberately bought some fruit to save you having to go
to the grocery.
This sentence is of the purposeful type and requires so that, although as pointed out above, you may just use so if you wish. Your sentence would look like this
I've bought some fruits so (that) you don't need to go to the grocery when you arrive.
(b) Oh! By the way, I happened to pick up some fruit, so you won't have to go to the grocery.
This sentence is of the cause and effect type and can only be completed using so. Your sentence would look like this:
I've bought some fruits, so you don't need to go to the grocery when you arrive
NOTE: In this case you require a comma before so unlike the previous version of this sentence.
You would need to decide for yourself which of these two scenarios is what was intended by the second sentence.