Parashara's Special Ascendants - Bhava Lagna, Hora Lagna, etc.

yes. The parivritti can always be done, its most important for seeing conjunctions, because, when a planet is conjunct in that chart it means it's exactly multiple of 12 divisions away from the conjunct planet. The method that is not parivritti are more important for seeing the planetary lords of things. 

YEs, they are both valid. 

yes, HL is a jaimini technique used to determine short, medium or long life. Here is the correctly translated technique which you will not find easily as most of jaimini is not decoded successfully.

2.1.1-2.1.14

Longevity - Method of Pairs



2.1.1. Aayuh pitridinesaabhyaam.

aayuh – Nom. life. pitri – (1). dina – day. iisaabhyaam – Abl. Dl. lord. (dinesa –  lord of the day, the Sun.)

Life from the lords of the lagna and Day. 



2.1.2. Prathamayoruttarayorvaa diirgham.

prathamayoh – Loc. Dl. first. uttarayor – Loc. Dl. next, last. vaa – or. diirgham – Nom. long.

Both in the first, or in the next and in the last – long.



2.1.3. Prathamadvitiiyayorantayorvaa madhyam.

prathama – first. dvitiiyayor – Loc. Dl. second. antayoh – Loc. Dl. end. vaa – or. madhyam – Nom. middling, intermediate.

Both in the first and second, or in the end – middling.



2.1.4. Madhyayoraadyantayorvaa hiinam.

madhyayor – Loc. Dl. middle. aadi – first. antayor – Loc. Dl. last. vaa – or. hiinam – short, deprived.

Both in the middle, or in the first and last – short.



2.1.5. Evam mandacandraabhyaam.

evam – in this way. manda – Saturn. candraabhyaam – Instr. Dl. the Moon.

In this way Saturn and the Moon.



2.1.6. Pitri kaalatasca.

pitri – (1). kaalatah – Nom. of Kaala (hora). ca – and.

And the Lagna and Lagna of Kaala.



2.1.7. Samvaadaat praamanyam.

samvaadaat – Abl. concurrence. praamaanyam – Nom. proven, evidence.

Proven by concurrence.



2.1.8. Visamvaadepitrikaalatah.

visamvaade – Loc. contradicting, contradiction, disagreement. pitri – (1). kaalatah – Nom. of the Kaala (hora).

In contradiction – the Lagna and Lagna of Kaala.



2.1.9. Pitrilaabhe candre candramandaabhyaam.

pitri – (1) laabhe – (7) Loc. candre – Loc. Moon. candra – Moon mandaabhyaam – Abl. Dl. Saturn.

The Moon in the 1^st or 7^th  – from the Moon and Saturn.



2.1.10. Sanau yogahetau kakshyaahraasah.

sanau – Loc. Saturn. yoga – (7) joining, union. hetau – (8) Loc. cause, by reason of, on account of. kakshyaa – zone.  hraasah – Nom. decrease.

Saturn therein, in the 7^th or 8^th – the zone decreases on account of the joining.



2.1.11a. Vipariitamanye.

vipariitam – Nom. reversed. anye – Loc. other, different.

Reversed in an other.



2.1.11b. Vipariitamityanye.

vipariitam – Nom. reversed. iti. anye – Loc. other, different.

“Reversed” in an other.



2.1.12. Na svarkshatungage saure.

na – not. svarksha – own rasi. tunga – exaltation. ge – (3) Loc. abiding. saure – Saturn (means coming from the Sun, as Saturn is the son of the Sun).

Not Saturn abiding in own rasi, exaltation or the 3^rd.



2.1.13. Kevala paapadrigyogaani ca.

kevala – only. paapa – malefic. drig – aspect. yogaani – Nom. Pl. union. ca – and.

And only malefic aspects and conjunctions.



2.1.14. Pitrilaabhage gurau kevalasubhadrigyogaani ca kakshyaavriddhih.

pitri – (1) laabha – (7) ge – (3????) Loc. abiding. gurau – Loc. Jupiter. kevala – only. subha – benefic. drig – aspect. yogaani – Nom. Pl. union.  ca – and. kakshyaa – zone. vriddhih – Nom. increase.

Jupiter in the 1^st, 7^th or 3^rd, and only benefic aspects and conjunctions –zone increase.