The torso pattern of the buff coat is ready, however I couldn't find a curve needle. Would a baseball stitch be a suitable replacement?

You can make your own curved needles.

Curved needles can also be found at most craft and hobby stores, as well as Walmart. They may be described as 'upholstery needles'.

Never mind I found some curved needles. Here is a photo of the torso held by duck tape. Is it too big? And does anyone know where I can find patterns for pre bent arm sleeve with integrated gussets?

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That's a good start, looking nice. Best of luck with the rest.

Here is the nearly complete coat. However, I am having problems with the armpit as its bunches up when I lower my arms. How to I correct this problem? Should I Leave a cut in the armpit and cover it with layers of cloth?

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Maybe you shouldn't make too much of a fuss about it if the bunching doesn't actually compromise your comfort or range of motion. It's precisely this bunching that gives you the extra material to let you raise your arms without lifting the body of the garment along.