Can I add priming sugar to a finished wine to carbonate it when I bottle it? I plan on fermenting about a month before I bottle it, would the yeast still be alive at that time?
Yes, it is entirely possible to make a sparkling fruit wine by adding sugar to the fermented brew before bottling it. I prefer to use glucose but table sugar(sucrose) or syrup(invert sugar) can be used as preferred. If a strong glass bottle is not available I recommend using PET fizzy drinks bottles. I do not recommend using "normal" beer or wine bottles as they are not designed for the higher pressures found in carbonated wines - but it does depend on how fizzy the wine is made. It is also important to make sure the wine has FULLY fermented before adding priming sugar and bottling. If the fermenting wine was left in the brew bin (or whatever the wine is being fermented in) for about 4 weeks then that is a good "rule of thumb" but it is better to use hydrometer to the determine the Specific Gravity. The fermentation has finished when the specific gravity remains constant over three or so days.
As a guide I use 350g of sugar or glucose to 24 L of fruit wine. That produces a fizz but not an eruption on opening the bottle. If you like it fizzier then 400 g of sugar can be used for 24L. Increasing the priming sugar to 450g usually produces too much carbonation to safely or usefully open the bottle inside the house. On the other hand it is perfect if you plan to celebrate winning a F1 Grand Prix.
In normal conditions after a month fermenting at "room temperature" the wine will contain enough yeast for successful secondary fermentation and carbonation. There is normally no need to add any yeast.