How to know that 'to' is infinitive particle or preposition?
In an infinitive, the X in to X will be a verb. If it's a preposition, X will be a noun.
Nouns often have articles or other determiners in front of them, if one of these exists for X, to then has to be a preposition.
I walked to the park - the is an article and that only appears in front of nouns.
One thing you can do with verbs here that you can't do with nouns is put an adverb like definitely in between to and X.
I walked to the park - I walked to definitely the park (doesn't work)
I wanted to go - I wanted to definitely go (work).
Also, the only form of a verb that can go after to is the plain form. The -ing or past/past-participle forms can't have to in front of it and make an infinitive.
To walk - might be an infinitive
To walked, to walking - never an infinitive, generally wrong.
Perfect infinitives with to have X'ed are OK; progressive/continuous with to be X'ing is also OK. But to X'ed or to X'ing is not OK.
So 1 and 3 are correct.