If my PRNG passes most or all diehard tests does it mean it is secure enough for practical usage? Should I test it with other programms, to ensure it's security?
Results of tests: http://pastebin.com/EzY7Pqjq
What do you mean, "secure enough"?
If you're thinking of cryptographic use, then arguably nothing short of "somehow convince quite a number of known brilliant cryptologists to spend lots and lots of time trying to break your PRNG and fail" will suffice as a test. Or you could just used one of the several off-the-shelf PRNGs that have already been subjected to this test.
If you're just using your random numbers for things like Monte Carlo simulations, or resilience against pathological input conditions, then the required standards are not nearly as high, and the Diehard tests are probably fairly reliable.