Learn English – Is “… and go to work by car.” correct in this sentence

This is the correct form. The verbs get, walk, put aren't present-tense forms but unmarked infinitives (unmarked means they aren't 'marked' with to). That is one of the two verbforms^† which are permitted in clauses which act as complements to most verbs of perception, like see, hear, notice.

It is sometimes difficult to distinguish an unmarked infinitive from the plain present form, because there is only one verb in which they are different: be, whose plain present form is are.

But when, as in your example, the verb's subject calls for a 3d-person singular form, it is easy to tell the difference. If these were present forms, the sentence would read

... he saw the man gets out of the car, walks slowly along the footpath at the edge, and puts a hand on a rail.

^† The other one is the present participle; you could also write

... he saw the man getting out of the car, walking slowly along the footpath at the edge, and putting a hand on a rail.

But the participle is usually used to say what someone is doing at a particular moment, not a series of things done; so the infinitive is preferred here.

You're missing a word:

"Do not wish for something more than you work for it."

The issue here is that "wish for something" and "work for (it)" are essentially independent clauses, and the "for" after "work" has to refer to something in the same clause.

(Some people will tell you you can't finish a sentence with a preposition, but this is not true. However, the preposition does have to point to a noun or phrase somewhere.)