Here are two questions regarding 2nd order linear DE's:
Regarding (5), I believe the only requirement for the roots of the CE are that they be real, and negative. If they are complex, we may write the solution without trigonometric functions, and no oscillation will occur.
Regarding (6)a, I believe we need the equation $\frac{dF}{dt} = \frac{1}{10} (70 -F(t))$, which solved yields $F(t) = c_1 e^{-\frac{t}{10}} + 70$ with $t$ in hours. Now I'm not sure what to do now, as using $y(0) = 70$ yields $c_1 = 0$, which naturally isn't correct. Any suggestions helpful.