You need a lot of steel supports. Plus the interior aisle room doesn’t look usable. A person can’t bend over and open anything in there standing in front of it.

That is not built to support stone, or anything, really.. You need actual cabinets and a pony wall. The ply is too thin for cabinet walls, or to provide vertical weight support. It would collapse. The interior room of the U is insufficient for function.

The current top appears to be supported by a 1/2" thick sheet of plywood. It's barely enough to hold up the plywood. So no to a heavier top. Those shelves are going to sag before you put anything in them. There needs to be face framing added to make it more stable, which will also hide all of the shelf cleats and screws.

You should have used 3/4" plywood OR made some simple cabinet boxes that were placed next to each other. If your cabinet boxes were made with 1/2" plywood, then every set of boxes butted next to each other would have been = 1" of plywood (although, I don't think I've ever heard of 1" plywood).

Did you pay someone to build this for you? If yes, how much did you pay? Also, did you have a contract?

I'm not a big woodworker - a bar can be made using kitchen cabinets + adding a pony wall behind them for the raised bar area (the same way builders make two level islands in a kitchen) or a frame can be built using dimensional lumber + plywood.

Frame made out of dimensional boards:

Shelving added to the frame:

Plywood used to cover frame (1/4" for sides + 3/4" for top):

He used laminate flooring to cover the plywood to make it look like the bar was made with nice wood:

The person below used cabinets and then added a pony wall built out of dimensional lumber:

Finished bar below after adding rustic wood planks to the sides + adding a countertop:

Here is all the plywood and dimensional lumber used to build a bar frame:

Here is the bar frame before any side plywood pieces were added:

The below bar is made with kitchen cabinets + foating shelves. A bar with a counter could be added in front of it if you wanted people to be able to sit at the bar. You'd use cabinets and build a pony wall (as shown in one of the examples above).

There are even bars that look nice that have been made out of IKEA cabinets. You just have to do a search. Wouldn't be that expensive (more than building a frame and covering it with plywood. All of the examples could have a counter added. Islands are made with overhangs by using metal brackets attached to a strong base.

The above two ways are how your bar should have been built. I really hope that you didn't pay for your bar. If it was a DIY - you could reuse some of the wood + pull up DIY bar building videos.

How much space should be between the back bar and front bar?

Seems you have built a custom bar in what would have been a dining room and I presume it will be used by you and a friend or partner. The space should be based on you and your sizes, not on a random specification.

Place items on all levels of the fridge shelves and both sides of the bar shelves. Try bending down to get something from the bottom of the fridge, does your backside hit the bar behind you? Can you bend down to load lower shelves and get things from them?

I am hoping this set up was made by a friend who only invested time and not money into it. Bottles of liquid weigh a ton, and glasses can get extremely heavy too. There is no way this bar is standing up to actual use. It honestly looks like a kids' play set up. If you need to start over, post your plan here. You can do better on the size and scale of the shelves against the wall.

A person bent over’s tush should not contact the counter opposite when standing behind the open door of the appliance. That generally starts at 42” of space. 48” is better if there would be 2 people behind the bar.

The non structural ability of that whatever it is to even support even itself is a RED FLAG that zero cabinet building knowledge is on board. You'd do better to use pre built cabinets, and learn how to build a pony wall. It at least has the ability to support something, and room to run the required electrical wiring. Which also seems to be lacking.

A bowl of chilli and the subsequent gaseous expulsion would blow that over. It cannot even support very thin plywood for a counter. It has no structural integrity for housing or supporting anything.