Yes In Shulchan Aruch YD 214 is stated that
אבל הנוהגים איסור בדברים המותרים מחמת שסוברים שהם אסורים לא הוי כאילו קבלום בנדר
If someone was acustomed to prohibiting something that is permitted by mistake, it is not as it he accepted a neder upon himself.
For hatarat nedarim if someone want to stop a minhag (when he was regarding it for himself as a duty, or his family was) See SA YD 214 . In this siman multiple cases are treated, for instance about allowed things, which someone considered by minhag as prohibited, or optional action which he considered as mandatory. The sources for Halacha are Mishnayot in the 4st chapter of Massechet Pessachim and a Brayta in the second chapter of Nedarim. But all this is for minhagim of a whole community, or region, and switching from one to another, or for family minhagim.
But for personal Chumrot, i.e. things which are known as allowed, and someone wants to be stringent, in way to protect itself from prohibited similar things. For this matter, Beit Yosef YD 214, at the end of the siman report in name of the Rashba and Ran that it is more strong than minhag and a simple hatarat nedarim does not be sufficient to cancel the prohibition.
We have not yet found the notion of 3 times, one time seems sufficient if he take it as a duty. Poskim said to specify to himself if he make something stringent, to say that it is not a neder and that it is not for ever but for one time. Buy I have found a Mishna which said a similar rule for a positive mitsva that he has to do it forever
after the first time.
The Mishna in Shekalim says (1, 3) See here and here:
כָּל קָטָן שֶׁהִתְחִיל אָבִיו לִשְׁקוֹל עַל יָדוֹ, שׁוּב אֵינוֹ פּוֹסֵק .
That one who had paid "the Half Shekel" for his minor son, cannot stop {and need to pay every year until the son comes of age to pay for himself.}
For the tefilin of Rabenu Tam, if he hasn't the minhag from family or community, the SA OC 34, 2 and 34, 3 said that it is a Hiddur, not a Mitsva, so if he was thinking that it is a mitsva by mistake, it is not a neder, if he was aware that it is a Hiddur and taked this as a duty for himself, hatarat nedarim doesn't be sufficient, he need Sheelat Chacham to allow the neder.