sum chords naturally have to mute certain strings or if ur prob is like being unable to sound the 5th string in the G chord, then u have to practice moving ur palm away from the neck can try to position ur body to lean towards the guitar so can play.
as for the strings prob. new guitars string still haven't stretch yet. so u keep playing them, tuning them daily. or if u want to invest, go get a new string(most guitar is gauge 9). i happen to buy full string set from swee lee tat costs $6, i string myself(it sucks) and then the strings are much easier to press even if it is new. otherwise, just keep playing with those hard strings, it's training for finger strenght, always use ur pinky, and try not to slide so fast while pressing hard or u might cut ur finger.
for me i bought a kapok guitar, it is a classical guitar with metal strings costs $39 only. plays great, slim guitar with rather loud sound qualities(i fingerpick so should be softer than picks). but only tat it doesnt sound complete. when u play the bass.