If you handle a dead body and it had a disease, will you get the disease? and if so how long until the body will be safe to touch?

Determine what type of disease it is first. Fluid transmission is the most common but then again, most people who handle members are completely protected. It totally depends on what they died of. 

That depends entirely on what disease.  Not every disease just jumps off of things to infect you. And without exactly know what disease there is no further way to answer this.

Wear disposable gloves like the professionals.

The police now have a unit called computer forensics that looks at suspects search history.  The evidence they find is admissible in court and leads to convictions of people who carelessly sought answers on the web before or after committing a crime.

Usually,  when the body dies, any disease it had at the time of death dies with it. The dead body is no longer contagious.
Unless you come home some day and find a family member lying dead on the floor, you're not likely to ever touch a dead body until after it's been washed, disinfected, and embalmed. 
Coroners, undertakers, embalmers, doctors, nurses, and any others who might handle a dead body wear protective clothing and gloves while they're handling a dead body.

As everyone else said, it depends on the disease.  Is the disease diabetes?  Than the answer is no.  Is it anthrax?  Probably.  


Different bacteria and viruses infect different cells, and some survive longer in a dead body than others.  Some infectious microbes can only be found in the respiratory system, some can't survive long in a dead body.  


Anthrax and the bubonic plague spread easily from dead bodies.  HIV not so much.  

It has been known to happen, but disease by disease.

What WILL invariably kill you from Typhus is mucking out a latrine being barefoot.

You could and it is why we are not having funerals right now in the USA.

Depends on the disease