Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

Question

Let $B = (B_t)_{t≥0}$ be a standard Brownian motion started at zero, and let $X = (X_t)_{t≥0}$ be a non-negative stochastic process solving

$dX_t = 7dt+ 2\sqrt{X_t}dB_t$ with $X_0 = 0$,

and let $F(t,x)=tx^3$.

1. Explain why Ito’s formula can be applied to $F (t, X_t)$ for $t ≥ 0$.

2. Apply Ito’s formula to $F (t, X_t )$ for $t ≥ 0$ . Determine a continuous local martingale $(M_t)_{t≥0}$ starting at $0$ and a continuous bounded variation process $(A_t)_{t≥0}$ such that $F (t, X_t) = M_t +A_t$ for $t ≥ 0$ .

3. Show that $(M_t)_{t≥0}$ in part 2 is a martingale and compute $⟨M,M⟩_t$ for $t≥0$.

4. Compute $\mathbb{E}(\tau)$ when $\tau =\inf\{t≥0:X_t =|5−4t|\}$.

My attempt:

1. Can apply Ito's as $X$ is a continuous semimartingale and $F(t,x)$ is a twice continuously differentiable function.

2. Applied Ito's to get

$$tX_t^3 = \int_0^t(X_s^3 +33sX_s^2)ds + \int_0^t 6sX_s^{2.5}dB_s,$$

where $M_t = \int_0^t 6sX_s^{2.5}dB_s$ and $A_t = \int_0^t(X_s^3 +33sX_s^2)ds.$

3. I have that

$$⟨M,M⟩_t = \int_0^t 36s^2X_s^5ds$$

but I'm not sure how to prove that $M_t$ is a martingale?

4. I'm not sure what to do for this part either?