With conditionals (IF ... THEN), like your first example, the 'rule' (it's far more complicated, really, because some specific situations call for different constructions) is that the tense-bearing verb in the condition (IF) clause and WILL in the consequence (THEN) clause take the same past/non-past tense:
If the price goes [non-past] up I will [non-past] buy it.
If the price went [past] up I would [past] buy it.
If the price had [past] gone [perfect] up I would [past] have bought [perfect] it.
It is the function (IF or THEN) of the clause, not its position in the sentence, which governs:
I will [non-past] buy it if the price goes [non-past] up.
I would [past] buy it if the price went [past] up.
I would [past] have bought [perfect] it if the price had [past] gone [perfect] up.
Note that will here does not express tense; it implies consequence, not futurity. You may substitute may/might or can/could for will/would in all these examples.
The situtation is different in your 'shopping' example, where will/would in the subordinate clauses does express tense, and must be deployed accordingly. Let's look at two different situations:
She told me last week that she would go grocery shopping yesterday, but I told her her I would not be able to go with her.
In this case the shopping trip was in the future when you spoke with her but is no longer in the future; you must employ the past form of will.
She told me last week that she will go grocery shopping tomorrow, but I told her I will not be able to go with her.
She told me last week that she will go grocery shopping tomorrow, but I told her I would not be able to go with her.
In this case the shopping trip is still in the future; you were unable to accompany her then and you still are unable to accompany her. You may use either will or would, depending on which timeframe you want to communicate.
No, you cannot shorten it. The explanatory that is as here:
That is, if you choose present tenses, ...
is the anglicised latin id est, which is usually itself abbreviated to ie or i.e.
i.e. if you choose present tenses, ...
As such, this usage of that is is a grammatical construction and should not be shortened.
So, while in general text and speech you can shorten that is to that's with an apostrophe to denote the missing letter in the contraction, you cannot shorten an explanatory that is.
Best Answer
Already may be used in any non-negative context, with any verb construction, simple, progressive, or perfect, with any time reference: it designates the time you are speaking about (technically, Reference Time).
In negative contexts, however, it is replaced with yet, unless you are explicitly contradicting a prior assertion with already.