In the US, the prosecution can appeal sentencing and pre-trial, but once you get to 'not guilty' or 'guilty', all prosecution associated with a crime is no longer constitutional.

However, you can get a civil trial after a not-guilty criminal trial (OJ Simpson was 'not guilty' in criminal court and became untouchable, but was found to have killed under civil court and had to pay the victims families).

From a prosecution perspective, the federal charges were a huge mistake. Nothing about the crime qualified it as 'federal homicide', so they had to settle for lesser charges. Normally the DOJ would back off and let the state handle it because it firmly falls in their jurisdiction, but of course this DOJ wanted to throw its weight around and it backfired on them.

It would be fairly awful given the circumstances. We have a history of faulty and overzealous prosecutions especially against black and poor people. For any given offense there are essentially 3 sorts of sentences. The sentence they will threaten you with in hopes of getting you to plea even if innocent say something absurd like 20 years, the "deal" you may be given which could be 3 months and the punishment for making them actually go to trial which may be 3 years.

Theoretically everyone is entitled to representation but you may not qualify for free help unless you are desperately poor and the quality of the free help may be so bad its worse than nothing. It's normal for unsuccessful prosecution to cost anything from thousands to hundreds of thousands depending on complexity of case. Ultimately virtually all cases are settled with a plea including cases which are so weak its hit or miss if they would have secured a conviction or sometimes cases so weak there was no chance of conviction but scared people accept it. Especially if its a case in which they get no actual time in jail they just agree to pay the government continually for years and go to jail if they ever get in trouble. Hell some people plea because the alternative is spending months in jail although innocent because they cannot afford to pay to get out but they get out immediately with a plea but agree to get robbed by the government for years.

In fact there is a sort of plea you can enter where you don't admit you did anything wrong but agree to go to jail anyway.

So if you understand just how fucked up our system is imagine if they can just keep going after going all the way to trial and definitively losing.

It's hilarious that our pres talks about shithole countries whilst presiding over one.

100% true but I was trying to explain the idea of double jeopardy then he brought up appeals so briefly tried to explain how that works

I am not a lawyer but in the US I believe once the verdict of not guilty is given the state is done. For example the oj Simpson case. Almost everyone agrees he likely did it but the jury gave the verdict not guilty because, according to interviews after, the state didn't provide enough evidence. They can't go back and say "sorry our lawyer was bad at his job, let's do a new trial". He was released and didn't face any criminal charges for the murder. Fun fact the Kardashians initially got famous/rich because the original father was one of oj's defense attorneys. Now they family of the victim later sued for emotional damage and won and he was also later arrested for other crimes but the criminal case of him killing his wife could/can't ever go back on trial.