A backshift normally takes place in reported speech, but there are exceptions. This very useful page lists some of the exceptions where no backshift takes place.

Rule 1: backshift of Simple Present is optional if the situation is still unchanged or if you agree with the original speaker.

Rule 2: Backshift of Simple Past and Past Progressive is optional if they cannot be mistakenly taken for backshift of Present Tense. So backshift is not necessary if there is a time expression indicating past.

Rule 3: Simple Past and Past Progressive do not normally change in sentences with when / if.

For your first sentence, this rule 3 applies.

For your second sentence, rule 2 applies to the second verb, but not the first:

I was thinking about helping her.
She said that she was thinking about helping her. - could be mistaken for backshifted present
She said that she had been thinking about helping her. - no mistake possible

I changed my mind later on.
She said that she changed her mind later on. - later on means no mistake possible

For the third sentence, rule 1 actually could be applied to both verbs. Furthermore, it could apply to what Joe said, because "wanting to know" is actually reported speech. We have three events:

• The man spoke to Joe
• Joe spoke to the writer
• the writer wrote down what happened.

If a condition has not changed between two events, a backshift is not required. For "wants/wanted", this depends on whether Joe told the man what kind of cigarettes we smoke (and so he no longer wants to know): for "smoke", it depends whether enough time has elapsed for us to maybe switch to a different brand of cigarette.

Looking first at Joe's report to the writer, for the first verb:

What kind of cigarettes do you smoke? - what the man said
He also wanted to know what kind of cigarettes we smoke. - joe told him He also wants to know what kind of cigarettes we smoke. - joe didn't tell him

For the second verb:

What kind of cigarettes do you smoke? - what the man said
He also wanted to know what kind of cigarettes we smoke. - yesterday He also wanted to know what kind of cigarettes we smoked. - twenty years ago

The first reporting gave rise to two possiblilities for each verb, so that's four possible combinations. The same criteria apply when the writer reports what Joe said, so altogether there is a total of 16 possible combinations: obviously, there will be some duplicates.

A backshift normally takes place in reported speech, but there are exceptions. This very useful page lists some of the exceptions where no backshift takes place.

Rule 1: backshift of Simple Present is optional if the situation is still unchanged or if you agree with the original speaker.

Rule 2: Backshift of Simple Past and Past Progressive is optional if they cannot be mistakenly taken for backshift of Present Tense. So backshift is not necessary if there is a time expression indicating past.

Rule 3: Simple Past and Past Progressive do not normally change in sentences with when / if.

For your first sentence, this rule 3 applies.

For your second sentence, rule 2 applies to the second verb, but not the first:

I was thinking about helping her.
... what she said
She said that she was thinking about helping her.
... could be mistaken for backshifted "I am thinking of helping her"
She said that she had been thinking about helping her.
... no mistake possible

I changed my mind later on.
... what she said
She said that she changed her mind later on. 
... cannot be mistaken for backshifted "I change my mind later on", because it doesn't make sense in this contenxt
She said that she had changed her mind later on.
... permissible but not necessary

For the third sentence, rule 1 actually could be applied to both verbs. Furthermore, it could apply to what Joe said, because "wanting to know" is actually reported speech. We have three events:

• The man spoke to Joe
• Joe spoke to the writer
• the writer wrote down what happened.

According to rule 1, if a situation is unchanged between two events, a backshift is not required. For "wants/wanted", this depends on whether Joe told the man what kind of cigarettes we smoke: if Joe told him, he no longer wants to know. For "smoke", it depends whether enough time has elapsed for us to maybe switch to a different brand of cigarette.

Looking first at Joe's report to the writer, for the first verb:

What kind of cigarettes do you smoke? - what the man said
He also wanted to know what kind of cigarettes we smoke. - joe told him 
He also wants to know what kind of cigarettes we smoke. - joe didn't tell him

For the second verb:

What kind of cigarettes do you smoke? - what the man said
He also wanted to know what kind of cigarettes we smoke. - yesterday 
He also wanted to know what kind of cigarettes we smoked. - twenty years ago

The first reporting gave rise to two possiblilities for each verb, so that's four possible combinations. The same criteria apply when the writer reports what Joe said, so altogether there is a total of 16 possible combinations: obviously, there will be some duplicates.

A backshift normally takes place in reported speech, but there are exceptions. This very useful page lists some of the exceptions where no backshift takes place.

Rule 1: backshift of Simple Present is optional if the situation is still unchanged or if you agree with the original speaker.

Rule 2: Backshift of Simple Past and Past Progressive is optional if they cannot be mistakenly taken for backshift of Present Tense. So backshift is not necessary if there is a time expression indicating past.

Rule 3: Simple Past and Past Progressive do not normally change in sentences with when / if.

For your first sentence, this rule 3 applies.

For your second sentence, rule 2 applies to the second verb, but not the first:

I was thinking about helping her.
She said that she was thinking about helping her. - could be mistaken for backshifted present
She said that she had been thinking about helping her. - no mistake possible

I changed my mind later on.
She said that she changed her mind later on. - later on means no mistake possible

For the third sentence, second verb, a slight adaptation of rule 1 might apply, because we probably still smoke the same kind of cigarettes. Really, this rule could be applied to the original sentence, because "wanting to know" is actually reported speech.

What kind of cigarettes do you smoke? - actual
He also wanted to know what kind of cigarettes we smoke. - reported

A backshift normally takes place in reported speech, but there are exceptions. This very useful page lists some of the exceptions where no backshift takes place.

Rule 1: backshift of Simple Present is optional if the situation is still unchanged or if you agree with the original speaker.

Rule 2: Backshift of Simple Past and Past Progressive is optional if they cannot be mistakenly taken for backshift of Present Tense. So backshift is not necessary if there is a time expression indicating past.

Rule 3: Simple Past and Past Progressive do not normally change in sentences with when / if.

For your first sentence, this rule 3 applies.

For your second sentence, rule 2 applies to the second verb, but not the first:

I was thinking about helping her.
She said that she was thinking about helping her. - could be mistaken for backshifted present
She said that she had been thinking about helping her. - no mistake possible

I changed my mind later on.
She said that she changed her mind later on. - later on means no mistake possible

For the third sentence, rule 1 actually could be applied to both verbs. Furthermore, it could apply to what Joe said, because "wanting to know" is actually reported speech. We have three events:

• The man spoke to Joe
• Joe spoke to the writer
• the writer wrote down what happened.

If a condition has not changed between two events, a backshift is not required. For "wants/wanted", this depends on whether Joe told the man what kind of cigarettes we smoke (and so he no longer wants to know): for "smoke", it depends whether enough time has elapsed for us to maybe switch to a different brand of cigarette.

Looking first at Joe's report to the writer, for the first verb:

What kind of cigarettes do you smoke? - what the man said
He also wanted to know what kind of cigarettes we smoke. - joe told him He also wants to know what kind of cigarettes we smoke. - joe didn't tell him

For the second verb:

What kind of cigarettes do you smoke? - what the man said
He also wanted to know what kind of cigarettes we smoke. - yesterday He also wanted to know what kind of cigarettes we smoked. - twenty years ago

The first reporting gave rise to two possiblilities for each verb, so that's four possible combinations. The same criteria apply when the writer reports what Joe said, so altogether there is a total of 16 possible combinations: obviously, there will be some duplicates.