Hello,
I would like to know which versions are correct:
(It's present - like a normal conversation.)
He told me you have a new job. :tick:
He told me you had a new job. :tick:
I heard you are a girl. :tick:
I heard you were a girl. :tick: (ambiguous; odd)
They said this is a good idea. :tick:
They said this was a good idea. :tick: (ambiguous)
I learned that "I thought you were a teacher." is correct, that's why I believe that all #2 are correct. 
Correct but ambiguous.
Cheers!
Let us see what one of the most authoritative and most comprehensive (1800 pages) grammar book of the English language has to say in this matter.
Quirk et al., (1985): p1026,
14.31.
Backshift in indirect speech
The reporting verb may be in the present tense for communications in recent past time, as in:
Joan tells me she is going to the airport in an hour's time. [1]
She says she was too busy to join us last night. [2]
The present tense is also used for reports attributed to famous works or authors which have present validity, as in:
The Bible says there is no end to the writing of books. [3]
Chaucer somewhere writes that love is blind. [4]
The choice of verb form in the reported clause depends on the time reference of the verb. Thus, the verbs in [1], [3], and [4] exemplify the state present, while 'was' in [2] refers to a time previous to the time of reporting as well as to the time of the original utterance.
Verbs of cognition may also be used in the reporting clause in the present tense:
I know they do not care.
Sylvia thinks Paul went to Lancaster last night.
When the time reference of the original utterance (or mental activity) no longer applies at the time that the utterance (or mental activity) is reported,
it is often necessary to change the tense forms of the verbs. Such a change of verb forms in indirect speech is termed
backshift. The resulting relationship of verb forms in the reporting and reported clauses is known as the sequence of tenses. The changes can be illustrated best if we postulate an exact correspondence for the reporting clauses of direct and indirect speech
DIRECT SPEECH BACKSHIFTED INDIRECT SPEECH
(i) present --> past
(ii) past --> past or past perfective
(iii) present perfective --> past perfective
(iv) past perfective --> past perfective
Thus, if the present deictic references in the direct speech become past deictic references in the indirect speech, there is a corresponding shift of verb forms into the past, or if necessary into the past perfective. Examples of each part of the rule are:
"I am being paid by the hour," she said. --> She said she was being paid by the hour. [5]
"The exhibition finished last week," explained Ann. --> An explained that the exhibition finished/had finished the preceding week. [6]
"I have been waiting for you over an hour," she told him. --> She told him that she had been waiting over an hour for him. [7]
"I had studied French for four years at school," I said. --> I said that I had studied French for four years at school. [8]
The choice in [6] represents the usual choice of simple past in place of a past perfective when the context makes the relative time reference clear, in this instance by the use of 'the preceding week'. There is no change in [8] because the past perfective already expresses 'past in the past' and no further backshift to 'past in the past' can be expressed. As [5] and [7] illustrate, the rule is not affected by combinations of the simple and perfective forms with progressive and passive forms.
Backshift is
optional when the time-reference of the original utterance is valid at the time of the reported utterance, cf [5], [7] and [8]. Thus the shift is obligatory in [9], but optional in [10]:
"I am a citizen not of Athens, but of the world," said Socrates. -->
Socrates said that he was a citizen not of Athens, but of the world. [9]
"Nothing can harm a good man," said Socrates. -->
Socrates said that nothing can/could harm a good man.
Since the statement by Socrates in [9] deals with what is now past, it has to be reported by application of the backshift rule. The statement in [10], on the other hand, is a universal rule which, if it was true for Socrates' lifetime, should also be true today; the backshift rule is therefore optional.
Here are other examples where present forms may be retained in indirect speech:
Their teacher had told them that the earth moves around the sun. [11]
Sam told me last night that he is now an American citizen. [12]
I heard her say that she is studying BA. [13]
A Yale professor has said that the Brooklyn Bridge is the most majestic embodiment of the American experience of the road. [14]
They thought that prison conditions have improved. [15]
I did not know that our meeting is next Friday. [16]
She said that they are being discriminated against. [17]
The waiter told me that lunch is now being served. [18]
In all these sentences, past forms may also be used, by optional application of the backshift rule. Sentence [11] has the simple present in its timeless use, whereas the verbs in the subsequent sentences have a limited time-reference. The appropriateness of the present forms [12 - 18] therefore depends on their reference at the time of the reported utterance. For example, if at that time Sam had changed his citizenship, or if his citizenship was then in doubt, an appropriate form of [12] would be, for example:
Sam told me in 1970 that he was then an American citizen.
Similarly, if a long time had elapsed between the original utterance reported in [15] or if there was doubt as to its present validity, the past perfective would be used:
They thought that the present conditions had changed. [15a]
Again, if [18] were reporting what the waiter had said not five minutes ago but five days ago, it would read:
The waiter told me that lunch was then being served.
NOTE:
[a] If the indirect speech itself contains a subordinate clause, then the verb of that subordinate clause may be in present tense because of current validity even though both the main verb of the sentence and the superordinate verb are in the past:
They
reminded us that they
had frequently
denied that the drug
has any therapeutic value.
She
thought she
had told me that breakfast
is served between seven and ten.
Backshift from simple past to past perfective is necessary when the simple past in the indirect speech may be misinterpreted as representing a simple present:
She said, "I was married (,but my husband died last year)," -->
She said that she had been married.
Contrast, where there is no possibility of misinterpretation:
She said,"I was married in church." -->
She said that she was/had been married in church.
[c] Backshift is normal if the proposition in the indirect speech is considered to be false:
The ancients thought that the sun moved around the earth, but from the time of Galileo it was known that the reverse is true.
[d] Since the simple past in indirect speech may represent either simple past or simple present of direct speech, it may give rise to ambiguity where both interpretations are plausible:
A She told me the game started at seven.
B: It did/does not
14. 32 Other changes in indirect speech
...
Guys, I have an important question.
I'm currently discussing the "reported speech" with some friends and there are disagreements.
One site says this:
Do you agree with that?
Does this "rule" (in case it's true) affect all the example sentences I gave?
He said that he has a new job. -> He still has the new job.
:?:
Cheers!
Backshift is optional when the time-reference of the original utterance is valid at the time of the reported utterance,
