As described in the beginning of this question, collenchyma cells are found in young stems and petioles (leaves) and function to provide flexible support to the plant. This is because chollenchyma cells lack secondary cell walls and do not produce lignin to harden them—this protein is characteristic of sclerenchyma cells, which are also used to provide support/strength to the plant. 

Due to their lack of rigidity, collenchyma cells a also capable of elongating with the stems and leaves they support, allowing them to remain alive at maturity. Sclerenchymal cells lack this ability.

As described in the background to the question, sclerenchyma cells are specialized to support the plant as it grows. These cells have thick secondary walls that are further strengthened by the hardening agent called lignin.  As a result, these cells are highly rigid and inflexible.  

At maturity, these cells cannot elongate and are found in regions of the plant that have stopped growing. In some parts of the plant, the sclerenchyma cells may even be dead; however, the rigid walls remain and act like a skeleteon that supports the remainder of the plaint over its lifetime.  

Sclerenchyma cells can also further differentiate into two types called sclereids and fibers. Sclerids can provide hardness to nut shells. Fibers, as their name suggests, are usually arranged in long threads and have commercial uses, such as being made into rope.

The vascular system in plants is designed to transport materials (water, nutrients, food) between the roots and shoots. There are two primary types of tissue dedicated to these processes. Xylem transports water and dissolved minerals upward from the roots; phloem transports sugars—the products of photosynthesis—from where they are synthesized to where they are needed, such as roots and new growth areas of leaves and fruits.

Both xylem and phloem are comprised of a variety of cell types that are specialized for transport and support. 

The stoma allows for gas exchange and transpiration. The stoma usually opens following stimulation by sunlight and closes in low water environments. Other answers are parts of a typical plant, however do not play a role in gas exchange or transpiration.

For proper functioning, plants must take in carbon dioxide, expel oxygen, and limit the loss of water vapor. This gas exchange takes place via pores called stomata. These pores are formed by a pair of adjacent cells that can open and close in response to a number of factors. These cells are called guard cells.

The cuticle and epidermis are layers of leaf structure, and do not correspond to specific cell types. The stoma is the name of a single pore itself, not its surrounding cells.

Parenchyma cells are the main photosynthetic cells of a plant, but also function in storage of water and nutrients. Parenchyma cells are usually soft cells that are located in leaves and fruit. Phloem cells contain sieve-tube members, and function in transport of water and nutrients throughout the plant. Schlerenchyma cells are strengthened with lignen, and are support cells.

The outer layer of cells on a leaf is called the epidermis. It is composed of the upper epidermis and the lower epidermis and the two have somewhat different structures and function, but both serve to protect the leaf from the outside environment. Spongy mesophyll and bundle sheath cells are both structures on the interior of the leaf, which house chloroplasts. Stomata are found on the outside layer of a leaf, but they are pores that allow gas exchange. Xylem is a transport structure that is used to conduct water and nutrients through a plant.

The mesophyll of a leaf contains palisade parenchyma cells (along with other cell types) which contain a high concentration of chloroplasts and are located near the edge of the leaf. These parenchyma cells in the mesophyll perform the bulk of the photosynthesis in a plant, though any part of a plant that contains chlorophyll can photosynthesize, including the spongy mesophyll.

The petiole attaches the leaf to the stem. Xylem is a tissue that transports water and minerals from the roots to other areas of a plant. Phloem is a tissue that transport water and nutrients from the leaves down to other areas of the plant. A filament is a part of a flower, not a leaf. Mesophyll is the tissue that makes up much of the body of the leaf and is where most photosynthesis takes place, but does not attach the leaf to the stem.

The mesophyll is the interior of the leaf. Chloroplasts are mainly found within the mesophyll and leaves are the major sites of photosynthesis in plants.