Translation:Don't explain it to me; I already understood everything!
The action, "Don't explain it to me; I already understood everything!", clearly states that explanation was already given in the past and hence the person wants that he/she shouldn't explain the thing again(in the present). Hence, it will be "understood" and not the present form.
I agree with BorealOwl.
While "I already understood" is not ungrammatical, this doesn't sound natural (at least to this American English speaker's ears).
It's a combination of the "already" in the sentence and the continuity of the verb "to understand". "I already understand" means that at some time in the past the speaker came to understand the idea. And during all the time from that point of understanding to the present the speaker has understood. So, stating "I already understand" implies that "I already understood"; they are somewhat equivalent. And it is more common in this type of present tense conversation for an English speaker to say "I already understand".
That said, I understand that it's a gray area in the translation and we're teaching French. So sticking with a one to one correspondence of the tenses (passé composé to English past) makes sense in that light.
I just think choosing a stative verb for this type of sentence for learning French can be confusing. It would be better with a non-stative verb like "to read": "Don't explain it to me, I already read everything."
If you take "already" out of the sentence, it highlights that the tense is wrong or the phrase is incomplete in the English response: "Don't explain it to me (now, present), I understood (back then? in the past? with the first explanation?)". "I already understand everything" sounds the most coherent, "I have already understood everything" clarifies the past tense, but "I already understood everything" sounds like a regional variation (albeit much of the US?).
The order of object pronouns before the verb in French is fixed regardless of whether they are direct or indirect objects. They appear in this order.
- me te se vous nous
- le la les
- lui leur
My first French teacher called this the Donkey rule because the y-en at the end sounds like the bray of an ass.