Hi! Is me! I’m gonna limit myself to one question per ask so hope this isn’t too much. Uh, first: if someone was, say, stabbed. After immediate first aid, when they’re not going to die any time, what would continued care and recovery time look like if it was done well but with no modern hospital equipment or medicine?
Since you said they're not going to die directly from the wound, I'm assuming they aren't bleeding internally, don't have holes in major organs, etc. In that case, the biggest risk with stab wounds tends to be infection. Germs get deep in there where it's hard to wash them out. So your number one priority is to keep this wound clean.
A lot of doctors actually won't stitch a puncture wound because stitches can seal bacteria into the wound and/or prevent the wound from draining properly. So if the surface area of the stab is relatively small (it's not gaping open and/or starting to bleed again every time you move), you're better off with just the pressure of a wrapped bandage to hold the wound more or less closed. Make sure to change bandages frequently and keep them as clean as possible. If sterile bandages aren't available, boil the bandages for at least 5 minutes and dry them in direct sunlight (hanging loose, not draped on a surface) before using them.
Clean the wound as thoroughly as possible when you change the bandages. If you have access to any kind of sterile rinse or antiseptic rinse, use that. If not, use hot soapy water; choose an antibacterial soap if you have one, and if not, choose one without any scents or perfumes added. Do NOT stick fingers, gauze, rags, etc. into the wound to try to clean it out. If you have a way to squirt slightly pressurized water into the wound (such as a bulb syringe or a water bottle with a pop-up mouth) you can use that to clean the wound more deeply. Rinse thoroughly after using soap. Dry the area around the wound and apply light pressure to the wound to remove any remaining water that seeps up, but don't try to dry out the inside of the wound. Some moisture is necessary for healing, and again, inserting any sort of gauze or rag into the wound is likely to do more harm than good.
Every time you change the bandages, look closely for signs of infection. There's likely to be some swelling and redness around the wound, but if those symptoms increase instead of decreasing, there might be an infection starting. You can also look for spreading size of the red/swollen patch, a darker red color, pus, increased discharge from the wound, or the wound starting to smell bad. The earlier you catch the infection, the better your chances of stopping it.
If an infection is just starting, cleaning the wound more frequently might be enough to stop it. Make sure to clean away any pus or loose infected material. If increased washing fails, finding an antiseptic becomes vital. Common first aid antiseptics tend to be harsh and can increase scarring, so they're not usually recommended for deeper/more serious injuries, but in this case we're assuming you don't have better options, so you can clean the wound using distilled alcohol (rubbing alcohol or high-proof spirits), hydrogen peroxide (3% solution is usually used for first aid), or iodine (also usually used in a solution of 1%-3% in an alcohol mixture).
If you can't find any modern antiseptics, a number of plants were used historically. Herbs such as garlic, rosemary, thyme, ginger, and cinnamon have antibacterial properties, but they tend to be more effective as preventatives than curatives. Still, it can't hurt to make an extremely strong tea with as many of those herbs as possible to help boost the immune system. Also make sure your patient stays hydrated and eats well to strengthen natural immunity.
As a last resort, you could also use a poultice made from any of the herbs listed above or from raw honey. Apply the poultice to the open edges of the wound but don't push it down into the wound. This is a historical technique with very questionable efficacy, but if you have no other options and an infection is getting worse, you can try it.
Recovery time depends on a lot of factors. A deeper wound takes longer to heal; so does a wound near a joint, since even small movements are likely to stretch or shift the damaged tissues. It'll take longer to heal if the patient can't rest consistently, doesn't get enough food, doesn't get enough hydration, or gets an infection. If we're assuming this wound is fairly significant, caused by a knife or similar dramatic mechanism of injury, you're looking at at least a week before the wound heals enough to let you regularly use the injured body part, several weeks if you're constantly on the move or get an infection, a month or longer before you can call it healed. Even then, there might be soreness, tenderness, or slight weakness of the surrounding muscles.