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.
Compare
(A) "If Anna was here, she would've known what to do."
(B) "If Anna had been here, she would've known what to do."
In (A), the speakers are currently considering what to do and lamenting that Anna isn't with them right now, because she would have been able to help them.
In (B), the speakers are discussing a past situation (we don't know how recent) where Anna's absence left them with no solution. The opportunity to do the right thing has now passed.
I think if you see the difference between the two, that will go a long way to helping you with similar constructs.
"If you (wear) a beard all the time, they (not recognize) you without it."
All the below are possible:
(A) If you wore a beard all the time, they would not recognize you without it.
(B) If you had worn a beard all the time, they would not have recognized you without it.
(C) If you were to wear a beard all the time, they would not recognize you without it.
(A) Can be used in a past sense, in a kind of confirmatory way: Given that you always wore a beard, then of course they wouldn't recognise you without it. But it can also be a suggestion for the future: if>then.
(B) In the past period referred to, he wasn't in the habit of wearing a beard, and therefore had no chance to pass unrecognised by removing it.
(C) More specific than the second sense of (A). Making a hypothetical suggestion concerning a group of people currently unknown; implying that at the moment he doesn't wear a beard all the time (or at all).
Best Answer
Those constructions are natural and idiomatic.
However, for me, the first example,
required me to reread it, since I initially parsed the sentence with:
instead of
By rearranging the parts of that phrase, it gets rid of that confusion;
You can similarly change positive "would have" statements into questions.
So,
and
can be transformed into: