I don't know much about composition and college, so I can't give you much information there. I can't give you much hope, either, so I'm going to give you critiques that I think are most appropriate.
College Audition Piece
M. 5-7: the left hand should be an octave lower because the right hand sometimes plays its notes and that's technically insane difficult. C# in m.6 does not fit well with the notes in the right hand because there are no chords in either hand and there should not be a prominent leading tone in both the melody line and the bass line. To fix this, I think an A in the left hand of m.6 should fix it. The resolution at the beginning of m.7 is weird, like @Monarcheon said.
m. 8: the left hand is also too high and share notes with the right hand. Not technically possible.
m.9 onwards: the figure in the left hand is not nice at a slow tempo, so you could change the tempo here. Also, the right hand does not need to play a triad from m. 9-10, as I feel it's unnecessary. A D in m.9 right hand is enough.
m.12: The dominant chord with a pedal tone in the bass isn't the greatest thing here, but it doesn't sound terrible.
m.14: the left hand change progression too late. This is fixed to an extent in m.15.
M.15: the right hand should begin with a dominant chord and not an inverted tonic chord. Also, there's a weird leap, though this isn't a weird issue.
m.18: I think this measure is unnecessary. I'm expecting the tonic chord here.
m.19: both hands start on a high note, which isn't a very logical idea because you're coming from below. Also, the left hand should play a vastly different rhythm from the right. This also applies to subsequent measures. The end of this bar and certain parts of subsequent bars don't sound son nice because the left hand doesn't fit well with the right hand harmonically. I can't explain what is wrong, but @Monarcheon could very well be right. Even I have difficulty understanding some of the language in that post, but that's my problem. m.22 is good.
The end is good, but this piece is too short overall and can be developped way more.
Rhapsody: Overall, I would like to see more complex harmonies, since you have more voices to work with. Everyone should play different notes except in special cases, and it's hard to write rules around those special cases.
m.1: The bass should always sound lower than the cello. Also, someone (either violin 1, violin 2 or viola) should play straight eighth notes for a better flow into m.2.
m.2: violin 2 moves above violin 1 and that is, unfortunately, incorrect.
m.3: viola drops out unexpectedly.
m.5: C# in violin 2 doesn't fit. I don't think it's a good idea to have such a note at the end of a bar and the harmony is D minor tonic chord.
m.6: The notes in the top 3 parts seem to be better suited for dominant harmony.
m.7: You can either continue using D minor chord for the bottom 2 voices or change F to E in violin 2.
m.9: it would be nice to have the viola play something other than D. The second violin and viola can hold their notes as long as cello or bass, or vice versa.
m.9-15: Mezzo-staccatos on 16ths would be very hard to execute unless done very slowly.
m.16: odd use of pizzicato. The cello should be higher than the bass and the two instruments share notes too much. This whole section is too static and can vary more harmonically, melodically and rhythmically.
m.33: the bass part does not fit with the cello part. It could play the same or similar thing as the cello. The resolution int eh next bar is weird because I'm expecting the E to resolve to D (tonic) and not Bb (submediant.
m.35-36: there's an augmented 2nd in the second violin. It still sounds okay, but it's theoretically incorrect.
m.37: too many As in upper strings. I think 2nd violin should play C# or G.
m.46: C and then C# sounds awkward.
The 6/8 section could be way more eveloped and there can be more harmonic and rhythmic complexity.
Test piece: The left hand could move more. This test piece is clearly incomplete and needs to be developed much further.
Theme: This is definitely incomplete and needs to be further developed.
m.1: The double bass should play the tonic note. Starting on an inverted chord is weird.
m.3: I think you want a dominant triad/7th chord here, or you could have the dominant triad/7th come in at the end of the bar.
m.5: Bass should resolve to the tonic chord.
m.5: Also applies to measure 2: As shuold be B-flats.
m.8: Bass should play tonic note.