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Yes, however the key to fitting any component is sticking to manufacturers torque settings, this is especially true with carbon products - it is relatively easy to over-tighten aluminium which can cut into carbon. Using carbon grip paste can help grip on carbon components where they interface with other carbon or aluminium.

Yes, providing they have the same bar diameter / stem clamp size (usually 31.8). While you can mix and match bars and stems, it does look nicer when they match.

No. Older quill stems worked with 1” threaded steerer tubes and are not compatible the current ‘ahead’ style stem / steerer interface.

Yes a carbon stem should work fine with aluminium bars, providing they have the same fit size, usually 31.8mm. Similarly carbon bars are fine with an aluminium stem. Take extra care to adhere to manufacturers torque settings when fitting, use a torque tool if you are unsure.

Providing the clamp size is the same as the handlebar diameter, technically MTB and road bars and stems can be switched. However! It is worth bearing in mind that the manufacturers intended use for a road stem is on the road, and likewise mountain bike components are designed for use on mountain bikes. Mountain bike parts are generally made stronger than their road bike equivalents, so it would be advisable not to use a road bike stem on an enduro mountain bike.

Yes, you can mix and match different bar & stem manufacturers, providing the have the same handlebar diameter and stem opening. Looks nicer when they match though!