First of all Panchadasi refers to a 15-lettered mantra. Among the three mantras that you have given only Mantra 1 is 15-lettered the others are both 16-lettered.
And, Mantra 2= Mantra 1+ Srim and Mantra 3= Hrim + Mantra 1.
To understand how these Sri VidyA Mantras are formed we first have to understand what is a Koota and what are the three Kootas.
A Koota is a combination of Beejas (Seeds). Like the combination "Srim Hrim Klim" (some say Aim Srim Hrim) is AdyA koota (It represents the Adi ParAshakti in Mantrik level).
The Panchadasi is formed by adding three Kootas viz: VAgbhava Koota+ KAmRaja Koota+ Shakti Koota. With each Koota being a combination of five seeds.
VAgiswari jyAna shaktir VAgbhAbe moksharupini |
kAmarupA kriyAtmikA ||
Shaktibije parA shaktiricchaiva shivarupini |
Evam devi trayakshari tu mahAtripurAsundari ||
In the VAgbhava koota or beeja Devi resides as Moksharupini,
VAgiswari-JyAnashakti. In the KAmrAja koota she is KriyAtmikA
kAmakalA- KriyAshakti. And in the Shakti koota she is Sivarupini Supreme
IcchAshAkti. In this way, Goddess MahAtripurasundari's [mantra] is
Trayakshari (three-lettered, since each Koota is also considered as an
Akshara, Panchadasi is thus three-lettered and fifteen-lettered both)
NityAshodashikArnava Tantram 4.17,18
Thus three Kootas represent the triad- JyAnashakti-KriyAshakti-IcchAshakti. They also represent the triad Sat-Chit-Ananda. ( For translation purpose- JyAna=Knowledge, KriyA=Action and IcchA=Will)
Now, depending on how these Kootas are combined, there are several Sri VidyAs that emerge. The mantra which start with the letter Ha is HAdi VidyA. The one which starts with Ka is KAdi and the one which starts with the letter Sa is called SAdi VidyA.
A brief overview of KAdi-HAdi-SAdi Vidyas is found here:
Kadi - Hadi - Sadi
[Query] Please enlighten about differences between kadi, hadi and sadi
In essence, there is no difference between kAdi, hAdi or sAdi as all
three refer to the same brahma vastu called srI lalitA.
kAdi was taught by Sri Manmatha [sadAshiva – nArayaNa – Hayagriva – Agastya - Shankara bhagavatpAda etc are the Gurus], hAdi by Bhagavati
Lopamudra [Parameshwara – Parashakti – Lopamudra – Kalatapanandanatha
etc. are the Gurus] and sAdi by Sri Krodha Bhattaraka Durvasa
Deshikendra [Mahadeva – Rudra – Durvasa – Dharmacharya etc are the
kAdi invokes kAmeshwarAmka sthitA kAmeshwarI, hAdi invokes kAmeshwarI vibhUshitAnko kameshwaraH and sAdi invokes kAmakAmeshwarau
shivau. In fact, Shadanvaya Shambhavi Krama described by Acharya in
Saundaryalahari is chiefly for sAdi upAsakas. The subtle differences
in these three visualizations should be learnt directly from one's
kAdi and hAdi panchadashi-s transform to laghu shodashi and maha/parA/guhya shodashi-s (in case of kAdi) and shuddha/hamsa
shodashis (in case of hAdi). There is no shodashi in sAdi karma but
the transformation is into saptadashI. Further, in the final step of
karma system, all the three paths merge into aS
The Mantra 1 is the Moola Panchadashi for the KAdi school. It was practiced by God Indra, Rishis Agastya and DurvAsa, for example.
KAmrAja Akhyaya vidyAya bAgbhabhe kAmbijam tyaktA chandram dadyAt |
KAmarAje punah shivAnte chandram...... | Tena shaktikootam
chandrendrakAmamahAmAyAtmakam | VidyemindropAsitA anyAt samAnam.... ||
In these above verses from JyAnarnava Tantram, Lord Shiva gives the codes of how the Mantra 1 in your question is to be formed or decoded. This mantra is practiced by DevarAja Indra.
The same mantra without the Bindus (Bindu the Dot) was also practiced by MahAmuni Agastya.
There are several other variants of Panchadasi or Sri VidyAs which were worshipped by Moon, Manu, Kubera, Brahma, Vishnu and Shankara etc. And not all of them are exactly 15-lettered. For example the Sri VidyA that is practiced by Vishnu is having six Kootas as opposed three in regular Panchadashi.
So, to answer your question, 1) is the correct version (KAdi VidyA), while 2 and 3 are not correct. Note that, by adding Srim Hrim beejas to the Panchadashi we can get the most powerful Shodashi mantra of Devi.
Additionally the mantra 1 in your question has GAyatri as Chandah (meter) and Sri Anandabhairva as the Rishi (Seer).