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There are a few things to do to care for your clematis in your area. Also it is helpful to know what cultivar you have, as some do better in your area than others. Here is a link that will help: http://web.extension.illinois.edu/cfiv/homeowners/051020.html

It appears to be root damage. It is possible that there are moles nearby. If there are no signs then of pests, then it sould be a fungal issue, but usually that affects the whole plant.

Here is an article that will help: https://www.gardeningknowhow.com/edible/vegetables/tomato/growing-indoor-tomatoes.htm

Are you looking for Clematis heracleifolia var. davidiana? There are also Clematis "durandii" and "Danielle". There are Ca nurseries which carry these. I could not find "Davidii".

It is best to wait until they go dormant, if you live in an area that gets some chilly weather. If not, then wait until the flowers bloom and drop to prune them.

Here is an article for more information: https://www.gardeningknowhow.com/ornamental/vines/clematis/pruning-clematis-vines.htm

Dividing is not how clematis are propagated. It is usually done by stem cuttings or layering. This is not a favorable time of year to use those techniques. Have you considered cutting down the plant and potting it up to move to your new location? Here is a step by step guide to division. http://homeguides.sfgate.com/separate-clematis-30039.html