My question is rather long but I would be really grateful if you could answer it because to me it is really important
I have been wondering if it is possible to say the sentences that I am going to write because I have never seen them written or even said maybe there is a nuance to note or maybe not, maybe they are right in formal speech but not in informal…if there is any of these nuances or other comment I will be grateful to read them:

The sentences are these:
1)It is impossible that he is there
2) It is impossible that he be there
3) It is impossible that he has gone there
4 ) It is impossible that he may be there
5) It is impossible that he may have gone there
6) It is impossible that he might have gone there
7 )It is impossible that he would do it
8) It is impossible that he would have done it
9 )It is impossible that he will do it
10 )It is impossible that he might do it
11( It is impossible that he had done it
12 ) It is impossible that he should be there
13) It is impossible that he should have gone to the party

Most of these make a little sense but they do not sound like typical English. I speak French, and I believe Spanish grammar is similar to French grammar. All of these sound like they could be direct translations of what a French speaker might say, for example.

#7 is the only one that you might expect to hear in everyday English. This because “It is impossible” sets a condition so you use the conditional form of the verb.
#1 might be possible with a good reason. (It is impossible that he is in Spain because I just saw him here in America an hour ago.)

#2 is wrong–no reason for subjunctive here. Most of the others just do not make much sense. “Impossible” is a very strong word; to say it with words of uncertainty like “might” or “may” does not make sense in English.

1)It is improbable that he is there
2) It is improbable that he be there
3) It is improbable that he has gone there
4 ) It is improbable that he may be there
5) It is improbable that he may have gone there
6) It is improbable that he might have gone there
7 )It is improbable that he would do it
8) It is improbable that he would have done it
9 )It is improbable that he will do it
10 )It is improbable that he might do it
11( It is improbable that he had done it
12 ) It is improbable that he should be there
13) It is improbable that he should have gone to the party

Most of these are awkward. “Improbable” is not usually used this way. Use “unlikely,” then some of these would sound OK. For example, #7 “It is unlikely that he would do it.” The conditional makes sense here precisely because the sense is conditional. None of the other verbs have that conditional sense. (“Should” is conditional but has the sense of duty, so it does not normally make sense with the word improbably or unlikely.)

And what about these??

1) I did it in order that he didn’t go to Spain
2) I did it in order that he might not go to Spain
3) I did it in order that he would not go to Spain
3 ) I did it in other that he could not go to Spain
4) I did it in order that he couldn’t go to Spain
5 ) I did it in order that he should not go to Spain

#3 are the only ones that works in English. This is also conditional.

Could I use the same way those sentences with ” so that ” instead of ” in order that ”

Only the #3 examples. Again conditional make the most sense.

Is ” would rather ” correct in indirect speech without changing the tense as in ” He said that he would rather not go to the party ”

This is good English and makes perfect sense. A Spanish speaker might say “He said that he would prefer not to go.” This means the same thing, but “he would rather not go” is more typical English.

I hope this helps.