Sandhyavandanam for those not initiated (without Upanayanam) using Puranas. It is possible?

Question

Many statements (eg. ŚB 1.4.25) talk of how non-initiated persons (irrespective of caste) cannot follow Vedic procedures, and how for them to read and follow, the Puranas and itihasas were composed.

A comment on a post about Navagraha tarpana provides a manual for 3 types of Sandhyavandanam procedures described in it:

In this pamphlet we give 3 forms of the Sandhyā the first is that of the Krishna Yajur Veda, the second that of the Sukla Yajur Veda and the 3rd is a Pauranika version which can be used by any one without any restriction whatsoever.

I’m interested in the Pauranika Sandhyavandanam procedure (given on page 24 of the manual), which contains mantras from the Puranas (not Vedas) except the Gayatri. The procedure is the same. The manual says that this Pauranika sandhya can be practised by ALL Hindus, irrespective of social circumstances:

Learning the Vedic mantras and their correct recitation is time consuming and exceedingly difficult and requires a competent guru, so in order to accommodate those who do not have the aptitude, inclination or the facilities for Vedic study and learning the complex Vedic liturgy and who still wish to live the religious life, the Agamas have prescribed a form of the sandhyā (daily prayer) that can be self-taught and used by everyone regardless of social circumstances.

Questions:

1. As stated in this manual, can the Sandhya as enjoined in the Puranas (using Pauranika mantras) be performed by non-initiates, without a guru giving deeksha of the Pauranika mantra?
   
   (Would like scriptural reference, preferably from multiple sources, saying this Pauranika Sandhya can be performed by non intitiates of all castes, men and women both)
2. Since the Gayatri mantra, forms part of the Vedas, can it be used, as instructed in Step 12 of the procedure, while reciting the Pranava and vyahritis too?
   
   Also, one can observe that in the Vedic procedure, the Gayatri mantra has Vedic accents. The Pauranika one lacks the accents, the mantra being the same (with the pranava and the vyahritis). In such a case what is the tune/ accent which is to be used while chanting the Gayatri, in case it is allowed?
3. Is the procedure described in the manual exactly endorsed by any of the 18 Puranas? If so which Purāṇa? (See Q4)
4. An answer gives a difference in the procedure described in two Puranas (one including Navagraha tarpana and one excluding). Thus, of the 18 Puranas, which one to follow? Is the procedure of the Purāṇa (Q3) which endorses the manual, correct, compared to the one we should follow?
   
   (Is it dependent on the sect (smarta/ Vaishnava) or God we worship?)
5. The Smritis enjoin compulsory Sandhyavandanam for dvijas, failing which a prescribed prāyaścitta must be performed. Is there any rule of compulsion (3 times everyday) for non-initiates (irrespective of caste) and the corresponding prayaścitta?

Answer 1

Regarding 2, if you're not initiated for gayatri, you can chant manas gayatri instead from Ramacharitmanas:

जनकसुता जग जननि जानकी। अतिसय प्रिय करुनानिधान की॥ ताके जुग पद कमल मनावउँ। जासु कृपाँ निरमल मति पावउँ॥

janakasutā jaga janani jānakī। atisaya priya karunānidhāna kī॥ tāke juga pada kamala manāvaum̐। jāsu kṛpām̐ niramala mati pāvaum̐॥