Ah, the question of the naive and inexperienced!!
Unfortunately, your questions are excellent but vague;
1) "rigid hallux limitus" There's no such thing. There's hallux limitus, and there's hallux rigidus, but I've never heard of rigid hallux limitus! Regardless, I have no one "favorite" procedure, because it all depends on the etiology of the condition. Each one of these conditions can be caused by different etioloties, including trauma, arthritis, metatarsus primus elevatus, an elongated first metatarsal, a long proximal phalanx, a previous surgery (iatrogenic), etc.
Therefore my procedure of choice is always dependent upon addressing the cause of the deformity. Each case is unique and has to be addressed accordingly. If the joint surface is not salvageable, I may perform a joint resurfacing such as NatCH. If the joint surface is salvageable, I may perform a decompression osteotomy.
Once again, it is always dependent on the etiology.
2) Low angle IM is usually an Austin type osteotomy, since I rarely perform "just a bumpectomy". Naturally, soft tissue structure releases are also performed. Medium angle IM deformities also include an Austin type procedure. For high IM angles I prefer a Lapidus. The type of fixation always depends upon the bone stock/density of the patient and the patient's "mental status", since not all patients can handle an external fixator on their foot. (You didn't ask about PASA so I didn't address that deformity).
3) Tailor's bunion. Once again this is dependent on the level of the deformity. Some are very mild and can be addressed with a simple "bumpectomy". Some can be treated with mini-tightrope as per NatCH and some with a mild increase in the IM angle can be treated with a mini Austin type procedure. However, some Tailor's bunions present with a "bowing" of the 5th metatarsal and must be treated with an oblique wedge osteotomy. So as previously stated, there unfortunately can not be one "favorite" procedure, since it is always dependent on the etiology.
4) Capsulotomy--that all depends upon what you are attempting to accomplish with your capsulotomy or if you are performing a capsule tightening procedure. Are you attempting to balance the area, de-rotate the area, etc?
5) Toe- Don't really have a favorite toe procedure, though I love a simple 5 minute arthroplasty.
6) I'm jealous of NatCH, because where I practice, there's NO WAY any insurance company would pay for an EXOGEN bone stim for every osteotomy procedure. They are only paid in my neck of the woods when there is a definite delayed or non union.
