Is there a breakdown of the simplification scheme into methods? For the second round of simplification (actually, its second part), there is a scheme dividing the processes into classes by the method used, such as:


leaving only part of the character that leaves the main impression;
retain the form and smoothen fine details;
replacing character altogether with a simpler one read similar;
replacing only a phonetic with simpler one;
use the hand-written form;
replace altogether by a new ideographic composition;
etc.


Is there a similar breakdown of how the simplifications were achieved for each particular one in the current list?
The second round is just a continuation of the first, so the methods involved are quite similar. For a break down of each simplified character and their corresponding method, you can check the Simplified Character Table 《簡化字總表》.
There are three sub-tables, the first one contains simplifications that can not be used as rules to simplify radicals in other characters; the second one contains characters that can be applied to others; and the third one shows the result of such application of rules.
The first table is most relavent to your question: see the Simplification Method column (簡化方法). For example 改換聲旁 means &quot;replacing phonetic radicals&quot;, 刪減偏旁 means &quot;deleting radicals&quot; (corresponding to the method &quot;leaving only part of the character&quot; in your list), and so on.