I'm learning piano, and I have a hard time to use two or more fingers together on one hand at the same time - there is a slight interval, e.g. when I play the first and third finger, there is a slight difference in when the two fingers hit the keys. Any help would be appreciated.
My professor had me slow practice four-note chords in each hand to fix this. For example: CEGC, EGCE, GCEG, CEGC (an octave higher than the first one), GCEG, EGCE, CEGC. Together with both hands, each hand an octave apart. Make sure that the notes all fall together, do it with all the keys. It's also a great exercise for pedaling; see if you can make the chords come out legato by use of the pedal. That should keep you busy for a couple of years. :)
The thing to strive for is, as you say, to hit all the notes at once with no uneven ones. Best way to do this is form all fingers on the keys, touching the keys. Then put the notes down by leaning into your hand. You'll start to see very quickly what the problem is. If the fingers aren't holding their weight, you'll have to work on strengthening them. However, the problem is just as often improper placement of the hands before you hit the keys. Try curving the middle finger more, flattening all the fingers, different things like that, with the idea that all the fingers drop with equal force and at the same time.
A more advanced exercise is to try to make different notes stand out in the chord, once you can hit them all evenly. Very often in music, you'll have chord passages where the melody is in the little finger of the right hand, and you'll need to make the top note of the chord a little louder than the other notes. That's an ability that you'll need to develop eventually. Bringing notes out of the middle of the chord is harder, but also important to be able to do.
Don't press the keys; place your hand in position, touching the keys and then drop the weight of your hand into the keys.
It's really just a matter of practice. Without seeing what's going on I would think that your fingers aren't as strong as they could be and some fingers are stronger then others. In this case just simple exercises like scales and arpeggios should be able to help.
If it's just a coordination problem then you can practice that by just practicing putting your fingers down at the same time. Just use the first 5 notes of the C major scale (C, D, E, F, and G) and practice playing two of the notes on the same hand at the same time. Once you get that down I suggest you move on to practice playing 3 notes at a time as chord will typically be composed of at least 3 notes and it is pretty common to play 3 notes on one hand.
If you have a MIDI keyboard and some MIDI recording software, you could use it as a feedback tool. Play some chords or intervals while the software records, and then analyze the MIDI data to see which note is being played first and by how much.
If the thumb is coming down first, try focusing on getting the third finger down earlier. Record your efforts and look at the results. It might be more helpful than trying to do it by ear or feel. As you repetitively get it "perfect", your muscles will remember how it feels and will do it naturally.