> Didn't Trump nominate the supreme court justice
Yes, nominating judges is basically the extent to which the judiciary is not independent, nominated justices are very much expected to act independently and without regards to who nominated them. Some examples of what Trump and Congress cannot do would be removing someone from the court, forcing the court to rule in a certain way, and so on.
> Also, didn't Trump himself say that he can intervene in Ms. Meng's case?
Trump regularly claims to be able to do things he can't in my experience - but yes. Trump can, perhaps, intervene in choosing not to prosecute Ms. Meng for a crime she did in fact commit. That's because how a court case works in the US is two sides argue their case to a judge. The judge is part of the judicial branch, but the side of the case representing the government is the executive branch of the government, which Trump is the head of. Prosecutors (the part of the executive branch that prosecutes people) have discretion towards which crimes they prosecute. With most prosecutions the president actually influencing the use of that power would probably be near impossible (but likely legal), extradition is more political as I understand it so he might actually be able to do so.
What Trump can't do is influence how that judges will react to the prosecution. If Ms. Meng did not commit a crime she will be found innocent (and indeed, if the government can't show that she committed a crime in a public trial with legally gathered evidence beyond a reasonable doubt). If the government can be shown to be knowingly maliciously prosecuting her despite her being innocent the attorney's involved will be sanctioned and she can likely sue the government for significant sums of money.
> What about the constant conservative vs democrat number battle in the supreme court?
This is basically entirely an unrelated internal politics thing. The US constitution is a rather vague document really, and as such there are some different interpretations. One party would prefer one set, another party would prefer another set, and they both try and nominate supreme court justices that will agree with their set. This has to do with things like "does the second amendment protect carrying handguns or just owning them". A "democratic" justice isn't going to be ruling on things because one side of a case is a democratic or anything like that.