Yes, but it is only temporary. This is known as an erection and is the result of being sexually stimulated. The swelling of the penis is from the blood going into it to make it erect.
No more than human hair gets longer if the person gets fatter. Whisker growth is not determined by how fat the cat may be.
You grow fatter by eating the foods which are high in fat. Also, if you don't eat a balanced diet you can grow fatter
There are no pills that will make the penis grow. The penis will grow at the speed, and to the size it is meant to be. The only way to make the penis longer is surgery, but doctors don't usually recommend it except in extreme cases.
You should take up exercises that makes your penis grow bigger but if you do them wrong you can really damage your penis.
When in Puberty the boys penis will grow longer and thicker.
A trees trunk will grow 'fatter' if it gets plenty of water. The more water the bigger ring of growth for the tree for that year.
Everything gets bigger as we grow older. Funny how nobody asks why our arms get longer or we get taller, isn't it? Possibly we need to quit obsessing about genitalia.
Noting that apples and oranges both grow on trees
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It begins to grow during the end of the first trimester in utero.
They grow taller, their penis grows longer, they grow body hair (chest, armpits, pubic region), their voice gets deeper, their hormones increase, their mental capacity grows more mature.
Overall penis length grows the most during puberty, commonly starting at age 8-12.