I'd hold your wrist *just* a bit higher, but that's more personal taste.
If you wish to keep your DIP joint (is this the nail joint? Either way this is still applicable) from collapsing, try playing from the literal tips of your fingers.
You may also consider playing some repertoire and exercises that is good for developing technique. For these, I would recommend Clementi Sonatinas, Op 36 Nos. 1 2 and 3, the Bach little preludes and inventions (if you haven't played the former, be sure to do so before studying the latter), Beethoven sonatinas perhaps... Oh, and Czerny etudes, no matter how boring they are, develop finger strength and develop it well. But better than Czerny for some purposes, is your.... Scales and arpeggios

All keys, 4 octaves, both hands, should be your end goal. First start with hands separate one octave if you must.
Many of the following things I mentioned are available for free in the form of a pdf here on PS. The Clementi is, the Bach inventions are, and the scales are. The rest is also probably largely available on musescore or noteflight. So, there's some stuff to get you started

If you choose to play those pieces, feel free to submit some recordings in the audition room!