Participles? Present participles? Are they nouns too? [duplicate]

A present participle can be used as an adjective or adverb as you do in your "rising sun" example, along with other uses (such as in the progressive present aspect).

A gerund can be used as a noun. Your "falling and rising" example is not actually a participle, but a gerund. Note that unlike nouns we would use adverbs with them, not adjectives:

Slowly falling and quickly rising.

A verbal noun is also used with a noun, but more noun-like in being modified by adjectives, subject to pluralisation, etc:

The callous killings.

Now, in English the present participle, gerund and verbal noun all look the same, as they are all created by appending -ing to the root, but they are distinct forms with distinct uses.