A friend of mine dropped of his guitar at my house for me to look at. It's some cheap beginners guitar that most likely came with a strap and an amp.
Anyway, the strings has been changed for the first time, and now there's trouble..

The harder i press down on the strings, the higher pitch i get. It's most noticable on the first 3 frets, and especially on the G-string. Does anybody have an idea here?

Would it help to deepen the grooves in the nut? Should I lower the bridge?

Any tips would be appreciated.

Apart from that there's the usual deal with bargain-guitars. The vibrato is floored all the way, so you can only slack the strings with the whammy-bar. Maybe I'll look at it, but I think I'll leave it since it's not my guitar
Actually, the pitch change is quite normal for guitars; especially at the bottom frets. This may not really be a problem at all. Lowering the bridge may be some help to reduce the chance of it doing that.