The molecules in this problem are isomers because they each have unique configurations and do not share the same funcitonal groups at the same carbon positions. Enantiomers are reflections of each other. Diastereomers are stereoisomers that differ at one or more stereocenters, while epimers are stereoisomers that differ at only one stereocenter.

Based on the Haworth projection given, the relative orientations of the three substituents are bromine up, hydroxide: down, hydroxide: up. In the most stable chair conformation, the largest substituents are oriented equatorial. If bromine is oriented equatorial up, the hydroxide at carbon 2 is equatorial down and the hydroxide at carbon 4 is axial up.

The two given molecules are conformational isomers. The molecules are superimposable by horizontally rotating either structure 180 degrees and rotating the bond between carbons 2 and 3. Both enantiomers and diastereomers are non-superimposable and constitutional isomers must have non-configurational differences in structure. There is no internal plane of symmetry, thus neither compound can be meso.

The most favorable chair conformation of a six-member ring is that in which the greatest number of large substituents are oriented equatorially. Conformation I corresponds to the given Haworth projection and orients all three large substituents in equatorial positions, making it the least energetic (most favorable) conformation.

There are four unique constitutional isomers possible for the given formula; meaning that they may not be made identical by conformational changes. They are illustrated as follows:

The anti conformation is most stable in a Newman projection because this is the form where the two largest functional groups are facing opposite directions and are furthest away from each other. However, note that in rare cases, such as in 1,2-ethandiol, the gauche conformation is more stable due to intramolecular hydrogen bonding. All other conformations have the functional groups closer to each other causing some repulsion and instability. The least stable of them all is the eclipsed conformation because this is the form where the functional groups are closest to each other.

In a Fischer projection, the groups on the left and right are coming out of the screen and towards the viewer. On the other hand, the top and bottom groups are going into the screen away from the viewer. One way to help you remember this is to think of the Fischer projection as a skeleton wearing one or more bowties (the skeleton is vertical and its bonds are drawn as dashes, which are going into the plane of the page/screen, and the horizontal bonds are drawn as wedges, which are coming out of the plane of the page/screen).