Circuit analysis (Current intensity)
The problem is that I can't even check if my answers are correct when doing a exercise. Is there any tool on internet that calculates such things ?

Yes, any SPICE-like simulator can solve this problem. LTSpice, ngspice, Microcap, and TINA-TI are four free (as in beer) ones that I know of. You can even use Circuitlab (the built in circuit editor attached to this site) to solve this problem.

Can you recommend any more secure and quicker way to analyse it ?

For the general case, no. What they're basically teaching you is how SPICE (and related simulators) solve this kind of problem. In the real world, you'll probably never solve a circuit with more than 3 or 4 resistors by hand --- you'll input it to a simulator and let the computer do all the matrix manipulation. But you should learn how the simulator works so you understand what kinds of problems it can and can't solve, what situations make it more or less accurate, etc.