Why is the 4.4 kb band barely visible in this HindIII digest of lambda DNA?
First of all, the 4.4 kb HindIII band is derived from the right end of &lambda; DNA, so during storage it anneals to the 23.1 kb left arm fragment via &lambda;'s 12 bp cohesive ends. You can solve this problem by preheating the markers to 65&deg;C for a few minutes then cooling rapidly (i.e. on ice). 

In a stained gel the intensity of a band is proportional to the amount of DNA in that band. This is why the heavier bands are more intense. The fragment X in lane 2 is similar in intensity to the 0.5 kb &lambda; fragment so DNA content of the two bands is similar.

The amount of DNA in the 0.5 kb band is 250 ng *(0.5/48.5) where 48.5 is the size of wild-type &lambda; DNA. I'll leave it for you to complete the calculation.