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We are given the horizontal distance from point $P$ to the tower, $d = 100 \, \text{m}$.
The angle of elevation of the top of the tower from $P$, $\theta_e = 15^\circ$.
The angle of depression of the base of the tower from $P$, $\theta_d = 1^\circ$.
We need to calculate the height of the tower, $h$.

Let $h_1$ be the height of the top of the tower above the horizontal line passing through $P$.
Let $h_2$ be the height of $P$ above the base of the tower.
From the angle of elevation:

From the angle of depression:

The total height of the tower $h$ is the sum of $h_1$ and $h_2$.

The height of the tower is $\boxed{\text{28.54 m}}$.

Let $R$ be the base of the tower.
From $P$, $R$ is on a bearing of $030^\circ$ and a horizontal distance $PR = 100 \, \text{m}$.
From $Q$, $R$ is on a bearing of $330^\circ$ and a horizontal distance $QR = 70 \, \text{m}$.
Points $P$ and $Q$ are on the same horizontal plane.

The bearing of $R$ from $P$ is $030^\circ$. Thus, the angle between the North line from $P$ and $PR$ is $30^\circ$.
The bearing of $R$ from $Q$ is $330^\circ$. Thus, the angle between the North line from $Q$ and $QR$ is $330^\circ$.

To use the cosine rule, we need the angle $\angle PRQ$.
Bearing of $P$ from $R$: $030^\circ + 180^\circ = 210^\circ$.
Bearing of $Q$ from $R$: $330^\circ - 180^\circ = 150^\circ$.
The angle $\angle PRQ$ is the difference between these two bearings.

In triangle $PQR$, we have $PR = 100 \, \text{m}$, $QR = 70 \, \text{m}$, and $\angle PRQ = 60^\circ$.
The cosine rule states:

The distance from $P$ to $Q$ is $\boxed{\text{88.88 m}}$.