Its very hard to be certain without seeing the guitar, but it sounds as if there are at least two problems.
If the strings keep going out of tune, nylon strings do stretch more than steel and do need tuning more when first installed.
Perhaps the knot at the bridge or the roller is loose.
Perhaps the neck is unstable and not straight and bends as you tighten the strings.
If the 1st fret is hard to play then it usually means that the slots in the nut (bone at the top) are too high. Its possible to check the height using this idea; viewtopic.php?f=11&t=64845#topic4
. Look at the section marked "Action".
"When I was younger, I could remember almost everything, whether it happened or not." Mark Twain