I understand what is written here; however, I do not know why "ci" is used in the following sentences:

La proposta che non ci si deve distendere sul marciapiede non è nè di destra nè di sinistra".

Io ci penserei bene prima di cambiare.

Grazie.........p

non ci si deve distendere
could be thought as
non si deve distendersi

think something like -self/ -selves

or kind of reflexive wrapper...
non si deve distendere se stessi sul marciapiede
non ci {si deve distendere se stessi } sul marciapiede

The second occurrence means about it

as in
pensaci bene prima di farlo

think twice about it before doing that

Ci penserei bene prima di farlo
expanded: {If I were you} I would think twice about it before doing that

Your first example can be explained as follows:-

If you want to use the impersonal with a non-reflexive verb such as fumare you say:
Qua dentro non si fuma.
In here one doesn't smoke, you(impersonal) don't smoke in here,

If the verb IS reflexive ( as in your example - distendersi), for example lavarsi then you say:

Qua dentro non ci si lava to avoid saying si si lava.
In here one does not have a wash, you do not have a wash in here.

Your second example can be explained as follows:-

pensare can be followed by di or by a:

Che pensi di quel film di Fellini? or if the film has already been mentioned then you would say Che ne pensi? (what do you think of it? What is your opinion of it?)

Penso sempre a quel giorno a Roma (I'm always thinking of (about) that day in Rome) or if the day has already been mentioned then you would say:
Ci penso sempre (I'm always thinking of (about) it)

So, to summarize, "ne" substitutes "di + something" and "ci" substitutes "a + something"

You need to be careful because in English you can say what do you think about that Fellini film? and I am always thinking about that day in Rome. In the first case you use "di" in Italian and in the second case you use "a".