Curious about the best ways to practice songs written for piano, i pay too much attention to the written rhythmic pattern and then I get frustrated since the rhythmic value written is not what my hands can play yet, should I focus on the notes and then add the rhythmic notation later? Your thoughts?
Pieces are made up of two basic elements - rhythm and melody. If either one changes, it's a different piece. Take a very simple kids' song, and just change the rhythm, keeping the same notes in the same order. Or keeping the rhythm, but changing some notes. A different song.
Try tapping out the rhythm as you look at a new piece. That way, there's no tune attached. When you're happy with the correct timing, play a phrase at a time. Hands separate, then together. It's not a good idea to play the tune in the wrong rhythm, for reasons mentioned earlier. And do it all at a tempo you can sustain, as slowing down doesn't help the learning process. I don't mean don't slow it all down - I mean don't start at a speed too fast to keep at. And keep counting. Even seasoned pros do that. Most of the time!
I'm concentrating to the chords and harmony, singing the melody and playing the rhythm as fine as possible. Playing the tune is the last priority. But this might be an individual approach.
During the learning process I think it's appropriate to modify elements to gradually build up to a full performance and also to explore the actual musical effect of various elements.
Simplifying a melody to just quarter notes can help you get the fingering changes under control. Simplifying the left hand to just block chords on half notes can help you understand the basic harmonic structure. You can do a lot of simplification and reduction in that way to feel out the essential musical elements. Once you have the 'lay of the land' you can then focus on the detail. This kind of process helps both with learning the mechanical performance, but also the musical structure.
Also consider breaking out certain passages that need special attention. For example, if there is a rhythm and chord change combination that is particularly trick. Focus on it. Play just those few measures fast, slow, legato, staccato, transpose it, etc. Maybe even invert the parts between right and left hands. Do it in the morning, then the evening. Be sure to take break from it with other material, but then go back to the problem area. That kind of contrast should help reinforce the training. Hit it from every angle you can until it isn't a problem.
And like @Tim said count out loud with rhythm practice. Use a metronome.