most reactions do not proceed by first the reactants turning into elements and then those elements turning into the product, nonetheless, when we calculate delta h, using that strategy we get the correct answer -- why

The answer is solid copper 

Answer( precipitate );

In order to improve results, many different steps can be taken into account. 1) using more precise scales and thermometers is always something that should be considered as being precise means that you are more exact with your answer.2) increasing the sample size should also be considered, if you have a bigger sample size you are able to determine if your results are accurate as well as if there are any variables that should be taken into account plus it assists in the statistical analysis and produces overall better data3) using better handwriting is also a plus, along with organizing the data properly so that others are also able to read the results and even redo the experiment in the future if it is needed.