Your first two questions are linked.
On most, if not all, yacht systems (and also the Holt Minireef, long since discontinued by the manufacturer) the spar does of course rotate around the forestay, and once rigged it remains standing at all times. The sail is then raised or lowered by means of a track in the spar, and a halliard.
The Helyar system is different in this respect, and indeed it differs between its two versions. In essence the spar rotates around the luff wire, not the forestay, and it remains entirely separate from the forestay; so the entire spar together with the sail can be removed from the boat without dropping the mast. With the Mk 1 system, the spar is slit along its entire length, and slides over the luff of a conventional headsail, trapping the luff wire inside the spar. With the Mk 2 version, the headsail is made with a separate luff wire, and an enlarged luff pocket which is just the right size to accommodate the assembled spar; the luff wire is then inserted inside the spar before the length is set and the final eye spllce is made, (and once both ends have their eye splices it cannot be removed from the spar without cutting), and the assembled unit is then placed inside the luff pocket of the sail.
On many dinghies and small cruising boats the headsail luff is very close to the forestay, and once proper rig tension is applied the forestay often becomes a little slack. Some attention to the detail is then needed in order to ensure that the slightly slack forestay does not get caught up in the roll as the headsail is furled. This problem can be prevented by a combination of two techniques; first, ensure that even when the rig is tensioned the forestay still has enough tension to remain just taut; On my GP14s I used to achieve this simply by careful setting of the forestay tension, but last week I saw two GP14s which use a short length of shockcord to take up any slack in the forestay, and that seems an easier and perhaps better system. Second, use of a spacer at the head of the sail to maintain adequate distance between the furled sail and the forestay.
Luff tension does of course involve two unrelated elements; the tension in the luff wire, and the tension in the sailcloth. The tension in the luff wire (the rig tension) is adjusted in whatever way one would use if no reefing system were fitted; the sail is hoisted, on its spar, and the rig is then tensioned in the usual way. On my GP14 I used to use an 8:1 muscle box, but many others use either a Highfield lever or a cascade tackle. At the other end of the scale, for the staysail on my Privateer 20 I use a loop in the fall of the halliard to give an improvised 3:1 purchase; that provides sufficient tension in this instance, and there are good reasons why I cannot use anything more sophisticated. I have no doubt that a toothed rack across the halliard is used by some owners, although it happens to be several years since I last saw that system in operation.
For the tension in the sailcloth, on at least the latest version of the Mk 2 the head of the sail is attached to the top of the spar, and a light lanyard is then used to pull the tack down towards the reefing drum, with just sufficient tension to pull out any creases, in exactly the same way as is sometimes done on a conventional headsail with no reefing. Once set, this adjustment will normally remain unaltered for the life of the sail. On the Mk 1, the tension in the sailcloth is adjusted by whatever method (if any) the sailmaker provided when the sail was made, and again will often remain unaltered for the life of the sail..
On your third question I am a little hesitant because I don't clearly remember how the spar is attached to the furling drum, but I can assure you that it is adequately attached. I think it involves a stainless steel clevis pin through holes in the spar and through the jaws on the top of the drum, but there may possibly be a spacer of some sort between the two. Two of the attached photos show the Mk 2 version (dating from 2017) on my Privateer, and should have sufficient resolution to enable you to expand them sufficiently to study the head and the tack detail.
I am not clear what you mean is asking "what stops the spar winding up", but if you are referring to potential twist in the spar that is adequately met by the torsional rigidity of the material and the wall thickness; the problem simply does not happen. In the days when I still sailed my GP14 I regularly used the system, reefed, in moderately strong winds, and at least once in full gale conditions moderately offshore, and never once had any noticeable issues of twist in the spar. The third photo shows A Capella sailing reefed on a blustery day in 2010, and there is no noticeable problem of twist there.
Hope this helps,