Hello Raviji, and all the users of this web... I want to share with you all my little knowledge about this matter. This are evidently the coded version of the mantras.The first "Dakṣiṇākālī" verses comes directly from the Devīrahasya (seventh chapter), or a really simillar text. They are the śāpavimocanamantra for the 16 syllabes (ṣoḍaśī) mantra of Kālī: kālīṃ (krīṃ) kūrcaṃ (hūṃ) paraṃ (hrīṃ) nāma dakṣiṇe kālike tatā || vaśiṣṭha mantraṃ proccyārtha mocaya dayamīśvari| kālīṃ (krīṃ) kūrcaṃ (hūṃ) pare (hrīṃ) nirameśā (svāhā) syāścāpahāriṇī || And the decoded śāpavimocanamantra for the Kālīṣoḍaśīmantra should be: krīṃ hūṃ hrīṃ dakṣiṇe kālike vaśiṣṭhaśāpaṃ mocaya mocaya krīṃ hūṃ hrīṃ svāhā|| The second part is the "bhadrakālī śāpavimocana mantra: "kālīṃ (krīṃ) bhīmaṃ (bhaiṃ) ṭhaṭaṃ (hūṃ) bhadrakālī bhīmaṃ (bhaiṃ) śivasyahi| śāpaṃ mocaya yugmāpo vidhyeyaṃ cāpahāriṇī || And the decoded mantra shoul be: krīṃ bhaiṃ hūṃ bhadrakālī bhaīṃ śivasyahi śāpaṃ mocaya mocaya||The Cinnnamasta verses doesn't come directly from the Devirahasya, but I think they are from a very similar or dependant text: vāsanāṃ kamalāṃ māyāṃ rudraśāpaṃ vimocaya| mocayāpo māyākyātāṃ cinnamastāṃka mocanam || And this is the Devi Rahasya version: vāgbhavaṃ (aiṃ) kāmarājaṃ (klīṃ) ca śivaśāpaṃ vimocaya| paraṃ (hrīṃ) niramiyaṃ (svāhā) vidya mumukhyāḥ śāpahāriṇī|| It's easy to see the similarity between both texts... tthe decoded mantra: aiṃ klīṃ śivaśāpaṃ vimocaya hrīṃ svāhā||Hope you and all the users of this page find this useful. I know that many are reluctant to reveal these mantras, but how can I? That I have found these mantras by chance, and all that I have is only by the mercy of my Goddess; how can I selfishly hide them from the sincere seekers.... PS: Sorry for my english, it's not my mother language and its a little dificult for me.

Excellent information

There is no need for homam for this procedure. 

Pranams Guruji. I have been doing Chaturavritti Tarpanam for the past 12 days. Your article has been very clear and useful. I want to know whether after performing for 44 days,should we have to perform homam? if so can I please know the procedure

Please do accept my humble pranaams to you on this auspicious day of Gurupoornima!

सदाशिवसमारम्भां शंकराचार्यमध्यमां। अस्मदाचार्यपर्यन्तं वन्दे गुरु परंपरां॥ sadāśivasamārambhāṁ śaṁkarācāryamadhyamāṁ | asmadācāryaparyantaṁ vande guru paraṁparāṁ || Beginning from Lord Sadāśhiva, through Śaṁkarācārya and up to our Guru Mandala, let us pay obeisance to all the Gurus. I invoke the Grace of our Guru Mandala be showered on you and your family on this auspicious day and everyday hereafter.  Thank you for your greetings.  

Namaste Sir, On this auspicious day of Guru Purnima, my pranāms to you and to all our Gurus in this paramparā and to Ma Lalitha MahaTripuraSundari Parabhataarika. In our tradition, Guru is the most exalted- compared to Bhagavān- an equivalent or even higher. I would like to take this opportunity to acknowledge and thank you for all that I have learnt from you and manblunder website. I am so glad that you are here for us answering our queries and teaching us. I pray that I will be able to meet you soon. Regards, Pratima

Can you please explain what is meant by "He is aware that ownership of actions does not belong to the living beings and therefore neither concerned with actions of others nor his own actions. He knows that he is either directly or indirectly responsible for such actions." as both are contradicting each other. He is not doing the work as Brahman is doing it but how then he is directly or indirectly responsible for it?

It is mentioned as dakṣabāhumūle (दक्षबाहुमूले), which means right arm pit. 

I think it is 100,000 repetitions for performing purascharana. In all the sessions you have to do nyasa, when you are doing mantra japa for purascharana.