After i replaced original focusing screen with a split one, it seems that every picture i take is overexposed now. Can it affect on exposure? Or i damaged something while replacing it? I own Nikon d7000.
It can and it does. The metering sensors are placed up in the top of the prism housing, in other words it reads the light AFTER the light has passed through the focusing screen.
If you are using a camera that is designed to have different mattes replaced (bad news: You are not) and the screen is one the camera is designed for, the necessary adjustments that have to be made to the metering to compensate for the screen will be pre-programmed into the camera and all you have to do is tell the camera exactly what screen you are using. But, alas, this does not apply to you.
If the effect of the screen was constant, ie "this screen eats one and one third of a stop of light", you could simply dial in this as the exposure adjustment and be happy. Alas, it is most problably not so, matte screens tend to have variable effect on the exposure readings depending on aperture.
This means that all auto and semi-auto modes on the camera will be affected by misleading meter readings. Which leaves you the option of shooting the camera in M mode... which is a lot easier than it sounds actually. I've been doing it for years. As long as the light is not rapidly changing, you can take a peek at the histogram every once in a while and adjust exposure so that the exposure is where you want it to be.
The great news is that you have not damaged anything, this is normal. The screen fits between the prism and the sensors and so it will affect something.
Using KatzEye screens as an example because I have personal experience on two Nikons, each has good notes on what kind of metering changes you will experience.
Mostly your exposure will change by a constant which can be adjusted for, mine were within within a small deviation of +-0.3, which is also good news for you.
With my screens spot metering becomes more complex, involving a little table of measured exposure versus fstop to define the compensation needed. The instructions suggest center-weighted and/or matrix metering on Nikons unless there's a pressing need for spot.