Problem : Where does glycolysis take place in a cell?

In the cytosol.

Problem : What is the name of the enzyme that catalyzes the phosphorylation of a glucose molecule in the first step of glycolysis?

Hexokinase.

Problem : In glycolytic steps one and three, what is the source of the phosphate groups that are added to glucose and fructose-6-phosphate, respectively?

In both cases the phosphate source is ATP. ATP molecules have three phosphate groups and after donating one phosphate group become ADP, a two phosphate containing molecule.

Problem : What class of metabolic reaction is catalyzed by phosphoglucose isomerase in the second step of glycolysis? What are the starting and ending molecules in this step?

An isomerization reaction occurs converting glucose-6-phosphate into fructose-6-phosphate.

Problem : In step four of glycolysis, why is dihyroxyacetone phosphate (DHAP) immediately converted into glyceraldehyde-3-phosphate (GAP) by the enzyme triosphosphate isomerase?

Of the two aldolase products of step four, DHAP and GAP, only GAP continues on in the glycolytic pathway. DHAP is converted to GAP so that it can continue in glycolysis.
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