Ok.

How many miles between oil changes - refer to your owners manual recommended oil change intervals and oil weights. If you lost it - good rule of thumb is somewhere between 4-5K depending on your vehicle's age, condition and what you use it for. Daily driver versus hauling heavy loads all day every day.  I personally know some people who change their oil every 3K, seems like over kill to me but nothing wrong with clean motor oil in your engine. 
Is there synthetic oils for diesels and gas cars or pick ups - Technically, yes. However, the biggest thing you will want to pay attention to is what your owners manual says is the recommended oil weights for your specific vehicle. Stick with that, and you will be good.
It is perfectly normal for your motor oil to come out black with every oil change. What you DO NOT want to see is little bits of metal in your oil (like fine glitter.) If you see that, there is something getting chewed up somewhere that needs to be corrected immediately before something catastrophic happens.
Scotty has awesome videos on his Youtube channel about motor oil weights, what they mean, the different applications etc. Search "Scotty Kilmer motor oil" and you'll see all his videos about it. Hope this helps!

I have a Jeep Liberty CRD (diesel engine), and the oil turns coal black a few days after an oil change. I change mine every 5,000-6,000 miles. It's got 170,000 miles on it, so I must be doing something right.

Hi.

I have a Jeep Diesel. I change my oil at 5,000 miles or six months, whichever comes first. I use fully synthetic that meets the requirements of my engine manufacturer. In my case that is 5w-30, MB229.51. 

My oil is as black tar within a few days of an oil change. The oil is doing its job keeping the engine clean and any soot particles in suspension. 

Use good quality filters. Fwiw, i use Mahle or Mann. 

On Diesel engine for cars and pick up trucks, how many miles should one change the oil?

Is there synthetic motor oils for diesel cars and pick upo trucks?