Answer: 1. Compound complex sentence.
2. The cat walked and purred.
Explanation: 1. Compound complex sentences have at least 2 independent clauses and one dependent clause combined by a comma and/or coordinating conjuction.
[After Molly lost the student council] - Dependent clause
[She decided to try out for soccer] - Independent clause
[Her friends thought she made a good decision] - independent clause
These sentences above are combined by a coordinating conjuction and commas.
2. The coordinating conjuction (and) is used to combine the two sentences therefore it is unnecessary to use the subject ( the cat) repeatedly.