Answers to Pepper34

1. argue in earnest (5 letters)
PLEAD

2. throw out solutions (10 letters)
BRAINSTORM

3. entity (5 letters)
BEING

4. meat-filled turnover (8 letters)
EMPANADA

5. similar in nature (11 letters)
HOMOGENEOUS

6. raise objections (7 letters)
STICKLE

7. barrel of monkeys (8 letters)
HILARITY