Where to begin.....?
OK. I get what you're trying to do.
The short answer is - it can't be done.
The long answer:
1) Is there a standard format for saving PLC files ( similar to DXF standard for
saving drawing files)?
There is no standard format. Allen-Bradley is the only one, that I'm aware of, that even imports from/exports into ASCII (which would be the basis of any "universal format".
Everyone's data structure is unique. Some have "unlimited" data registers. Others are fixed. Everyone handles timers differently: AB's which consists of a three-word element, GE's are three consecutive words, others allow you to assign the addresses. Some allow you to address the bits within a word, others don't.
It's a mess out there, and there's no standard.
2) Where can I find info about actual logic for executing a PLC program?
You can't. It's proprietary, closed, and protected. In theory, it's possible to hack it out. But I don't recommend it.
Are the components evaluated in ROW-COLUMN order or COLUMN-ROW order etc. ?
It depends on the brand. Most are row-by-row. Modicon is column-by-column. As I said, it's a mess out there.
So what I ideally would want to do is...[w]rite code specific to my hardware, so that my hardware can interpret the PLC program and execute the program.
I think you have a fundemental misunderstanding of what a PLC is and does. Although it IS a PC (sometimes even with an Intel x86 chip in it), it also ISN'T a PC.
You can't just download any old thing to one. It MUST be in the manufacturer's languange (not just on the IEC 61131-3 level, but on the assembly language level.
The PLC ONLY understands the instructiions in the manufacturers Instruction Set. Nothing else. Period. (Well, OK, years ago, AB had a program (called CAR) that might allow you to add to the instruction set of the PLC-5. I think about 6 units were sold.)
In figuring out what you are trying to do, I'm at a loss as to just where the "ladder-executing" program will reside. If you download it to your machine, how is the PLC going to get it's instructions to turn on motors, etc? If you are going to download it to the PLC, how does it communicate with your machine?
If you are trying to build a "PLC-like" interface to your machine, so that a programmer will use ladder logic rather than instruction lists, well..., OK..., but WHY? You'll be teaching any new programmer how to program your machine, regardless of the interface you create. Create the interface that makes the users life the easiest. If that's ladder, fine. If that's instruction list, fine. If you are doing sequencing, you might prefer Sequential Function Charts (also part of 61131-3). The thing about ladder is that it is intended to mimic relays. It helps to think of ladder as all the rungs executing "at the same time", and think of power flowing through the rungs.
If you are just trying to interface your machine with a PLC, then you need to understand commucation protocols. The OPC Foundation may be a good place to start.
But a PLC has a microprocessor. It sounds like your machine has a microprocessor. 2 microprocessors means 2 programs, with communication between them. It sounds like you are trying to write just one program.