Which instrument is used to measure the rate of transpiration?

Here are the answers to your questions:

1. The diagram shows a plant cell. Which part maintains the shape of the cell?
The part of a plant cell that maintains its shape and provides structural support is the cell wall.

2. By which process does water enter root hair cells?
Water enters root hair cells primarily through the process of osmosis. This is the movement of water from a region of higher water potential (in the soil) to a region of lower water potential (inside the root hair cell) across a selectively permeable membrane.
The correct option is A.

$$\boxed{\text{A osmosis}}$$

3. Which instrument is used to measure the rate of transpiration?
The instrument specifically designed to measure the rate of water uptake by a plant, which is an indirect measure of the rate of transpiration, is a potometer.
The correct option is D.

$$\boxed{\text{D potometer}}$$