First of all, it is "Punahcharana" not Puracharana. "Punah" means repetition and "Ucharana" means speaking/ enchanting. Together it will be Punah + Ucharana = Punahacharan, which means, repeating the enchanting.
This is mainly used as a revision exercise in ancient days of schooling.
In earlier/ ancient days of schooling, where there are no books, the study of vedas and other related subjects were through the Guru only. The Guru teaches the mantras, slokas as part of the education. Though he explains in detail, the meaning of every mantra and sloka, sometimes it will be hard to remember. So, they usually divide the students into groups, based on their remembering power. Ekasandyagrahi (Eka (one) + Sandya (time) + Grahi (who can memorize)) is a student who remembers everything even though he is listening it for the first time. Dwisandyagrahi (Dwi = two) need one more repetition of the teaching, and so on. Now, once the guru completes his teaching, these Ekasandhyagrahi's will repeat again the same so that Dwisanyagrahi's can takeover from there, and so on. Once in a while, the students group together and do the "Punahcharana" to revise the past teachings.
Now, let me answer your questions as far as I know. Anybody can correct me if I'm wrong in any of the point.
1. Can Purascharana be initiated even without a guru?
Ans: As per my previous explanation, yes. One can initiate a Punahcharana without a guru. But to correct if he is doing a mistake, doing a "Punahcharana" should be done in front of the Guru/ the Teacher. Especially, in the case of mantras where the phonetics play a vital role, the presence of Guru is a must.
2. Should the mantra be repeated fixed number of times daily? What if there is a variation in the no. of times every day?
Ans: "Punahcharana" is a revision exercise. For mantras, the student has to obtain the complete knowledge behind it and acquire the power of it. Until then there is no limit. For example, the great "Gayathri Mantra", generally, as a common practice, will be enchanted for 108 times a day. But you won't lose anything if you do it for more than 108 times. Sometimes, some brahmins will sit and do for more than a few thousands a day, to complete 1 Lakh times. Do you think the god will count while you are chanting. I don't think the gods will not curse you, if you miss for a few times. Our great Gurus created these numbers to improve the dedication towards the process. The bottom line is, it doesn't matter how many times you did it. The only thing matters is how you did it and what you got out of it.
3. What if he repeats without doing a sankalpa of the number of times daily?
Ans: In practical, as the name suggests "Sankalpa" is a dedication to do something. In a way, you are initialising a vedic ritual. If you keenly observe the "Sankalpa" process and it's meaning, you will come to know that it says for what purpose you are doing this ritual and which god/ goddess you are decided to worship during it. It is to create a feel in what you are doing.
4. Can he repeat the mantra in any posture, circumstance or place?
Ans: These are some important aspect in the doing any important work. Can you do a 4-5 hours ritual without sitting? During that, will you be able to concentrate after half an hour? Will you be able to concentrate on the process, if you are getting a pungent bad smell? Will you be able to sit without moving, if the place is not clean and its a place for insects (ants, cockroaches, etc.)? Considering all such situations, our scriptures created some rules on these aspects. Moreover, if you observe most of these postures are related to yoga, meditation and kundalini etc. If you have arthritis, you can do it in you home by creating some clean place where there is no disturbances from outside world. You simply lit a light and a incense stick to give a pleasant and peaceful mind.
5. Should the speed of repeating the mantra be uniform or is it enough if the mantra is pronounced with clarity?
Ans: Clarity and phonetics are very important for mantras. What you want to gain by speeding up the enchanting? What you want to gain out of it? If you have other important things than this, enchant for less number of times till when you have concentration. Or don't do it at all if you are unable to concentrate. No problem. The dedication towards the god and the process is important, nothing else.
6. Can he recall the mantra even within him (without speaking out)? Does this count?
Ans: He can recollect it anywhere and any time. Regarding the count, I have a question. What you want to do with the count? Think about about how many times you are awakening yourself with that knowledge.
7. If one chants the mantra by habit unconsciously, does this count towards Purasacharana?
Ans: Consiously or Unconsciously, whenever you are doing a revision of what you learned, you can call it a "Punahcharana".
8. Can he eat meat while doing Purasacharana? Doesn't this habit drop by itself when he reaches a certain stage?
Ans: Meat is not a "Sathvik" food as per the scriptures. They say that the person who want to do some vedic practices should not eat food which is not "Sathvik". Because, as per their experiences, if you want to control you body and your mind, you should eat only "Sathvik" food. And for the second part of your question, I don't think the habits will fade away just like that without that person's dedication. If you know what you are eating and if you are OK with it's effects, you may continue.
Finally, sorry for the lengthy post.