Greetings Milagra,

The best time to prune your clematis would be at the very beginning of spring or even late winter.

The reason for this also gets at the answer to your second question. Clematis stems are very fragile, and any type of injury (which happens easily when pruning) can cause the entire stem to die. However, stem dieback also promotes new growth during the spring, which is especially good for late-blooming clematis plants which bloom on new wood.

You could try to very carefully remove the old, dead stems now if they really bother you. Whenever you decide to prune, examine the dead stems for black spots which may point to a fungal infection called clematis wilt which can also cause stem dieback. The best defense for a fungal infection would be to ensure your soil drains well (amend with compost if necessary) and the roots do not stay very wet for long periods of time.

You can learn more about clematis care in this OSU Extension article:

https://extension.oregonstate.edu/news/how-grow-clematis-long-lasting-color-oregon-gardens

Happy gardening,