T-test - sample test - group statistics. Can I make a conclusion of this if my sign (2-tailed) is not significant? 
my hypotheses lower comprehending score for living out of home, higher distancing score for living out of home
The group statistics does show that my hypotheses were right but the sample test is not significant. What conclusion can I make?
 A: There is a difference between 1 sided tests and 2 sided tests. If you are testing a difference between two groups without having a hypothesis about the direction (which one is higher) then you will take the two-sided p value (significance value).
In your case, actually you expect that out home living has a lower comprehending score. Therefore you should compute the one-sided p-value (not given by some programs including spss) by dividing the two-sided p-value by two. This would give you 0.072 / 2 = 0.036 which is inferior to 0.05 (the usual significance level). Therefore you have shown that people living "out home" are on average less comprehending then those living "at home".
Concerning the second test, you have not been able to show that people living "out home" are more distancing then those living "at home". It may still be true (or false) but in any case with the sample that you have collected the hypothesis cannot be proved.
A: Assuming that scores are approximately normal, I checked your 'Comprehending'
data and got P-value (not assuming equal variances) indicating you can reject (5% level) the null hypothesis that
'In home' and 'Out of home' subjects have equal population means against the
one-sided null hypothesis the In home subjects have a higher population mean.
Two-Sample T-Test and CI 

Sample   N   Mean  StDev  SE Mean
1       80  2.765  0.592    0.066
2       53  2.563  0.680    0.093

Difference = μ (1) - μ (2)
Estimate for difference:  0.202
95% lower bound for difference:  0.012
T-Test of difference = 0 (vs >): 
    T-Value = 1.76  P-Value = 0.040  DF = 100

Assuming that the analysis for 'Distancing' is also correct, you could reject
(6% level) that the 'In' and 'Out' have equal population means against the alternative that the population mean for 'Out' is higher. 
It is not a Fundamental Law of the Universe that all hypotheses must be tested at the 5% level (although some journals insist on that for publication), so it may be worthwhile mentioning
this "suggestive" result. If the issue is sufficiently important to revisit, perhaps you would want to do a successive study (perhaps with more 'Out-of-home' students, or a more sensitive measure of 'Distancing') in hopes of finding a more definitive result.
Note: To be clear, I have no disagreement with your analysis nor with @Joos Korstanje's (+1) interpretation of the results. (Over years of experience I have developed a habit to double-check SPSS results, and I wanted to point out that your second result is 'almost' significant.)
