I want to invoke those C function or executables in python. Is that possible.

Yes, you can write C code that can be imported into Python as a module. Python calls these extension modules. You can invoke it from Python directly, an example from the documentation:

Python Code

import example
result = example.do_something()

C Code

static PyObject * example(PyObject *self)
{
    // do something
    return Py_BuildValue("i", result);
}

If I want the C code to be a library, which means I use it with #include and linkage of the *.o likely in python, how to do it or is that possible.

You build it as a shared library *.dll or *.so You can also investigate using distutils to distribute your module.

If I write the C code into executable, which means it becomes a command, can I invoke it in python directly?

If you write a *.exe then you are doing the opposite (invoking Python from C). The method you choose (exe vs shared library) depends on if you want a "C program with some Python" or a "Python program with some C".

Also, I heard that python code can be compiled, does that mean we can execute the code without the source file? Are the output files binary files? Does it improve performance?

Python reads *.py files and compiles to *.pyc bytecode files when you run it. The bytecode is then run in the Python virtual machine. This means "executing the same file is faster the second time as recompilation from source to bytecode can be avoided." (from the Python glossary) So if you haven't edited your *.py files, it will run the *.pyc. You can distribute *.pyc files without *.py files, however they are not encrypted and can be reverse-engineered.

I knew C before I knew Python. No offence intended, but I don't think that your C knowledge is that big a deal. Unless you read very, very slowly, just set out to learn Python. It won't take that long to skim through the material you're familiar with, and it's not as if a Python tutorial aimed at C programmers will make you a better Python programmer - it might teach you things in a different order, is all, and raise some specific things that you would do in C but that you should not do in Python.

Strings in Python actually are somewhat different from strings in C, and they're used differently. I strongly recommend learning them "from scratch", rather than thinking about them in terms of their differences from C strings. For one thing, in Python 2 it's best not to use Python's "string" class to represent strings: there's a separate unicode string class and for practical Python apps (pretty much anything involving user data), you need that. (Python 3 fixes this, making the str class a unicode string). You need to establish a good working practice for unicode/byte data and decode/encode.

A common mistake when learning a second programming language, is to think "I know how to program, I just need to translate what I do in C into Python". No, you don't. While it's true that an algorithm can be basically the same in different languages, the natural way to do a particular thing can be completely different in different languages. You will write better Python code if you learn to use Python idiomatically, than if you try to write Python like a C programmer. Many of the "tricks" you know that make sense in C will be either pointless or counter-productive in Python. Conversely many things that you should do happily in a typical Python program, like allocating and freeing a lot of memory, are things that in C you've probably learned to think twice about. Partly because the typical C program has different restrictions from the typical Python program, and partly because you just have to write more code and think harder to get that kind of thing right in C than you do in Python.

If you're learning the language because you urgently need to program a system/platform which has Python but doesn't have C, then writing Python programs that work like C programs is a reasonable interim measure. But that probably doesn't apply to you, and even if it did it's not the ultimate goal.

One thing you might be interested to look at because of your C experience, is the Python/C API. Python is great for many things, but it doesn't result in the fastest possible computational core of scientific apps [neither does C, probably, but let's not go into FORTRAN for now ;-)]. So if you're aiming to continue with scientific programming through your move in Python, and your programs are typically memory-bus- and CPU-bound doing immense amounts of number-crunching (billions of ops), then you might like to know how to escape into C if you ever need to. Consider it a last resort, though.

You do need to understand Python reasonably well before the Python/C API makes much sense, though.

Oh yes, and if you want to understand OOP in general, remember later on to take a look at something like Java, Objective-C, C++, or D. Python isn't just an OO language, it's a dynamic OO language. You might not realise it from comparing just C with Python, but dynamic vs static types is a completely independent issue from the OOP-ness of Python. Python objects are like hashtables that allow you to attach new fields willy-nilly, but objects in many other OO languages store data in ways which are much more like a C struct.