OK Tamarisk. I should really know better than to make categorical statements on these forums. I'd never seen or heard reference to aster cuttings but it seems that they do work. I Googled and interestingly there are very few refs to UK sources for this method of propagation. We just divide the clumps up. I still think the bits in the photos don't look very promisimg cutting material but there's no harm in having a go.

The plants should grow rather easily from seed. Just collect seed pods that are beginning to break open. In AZ there are 30 native species! Here is the list: A. albicans, A. angustifolia, A. asperula, A. brachystephana, A. cryptoceras, A. cutleri, A. englemanniana, A. erosa, A. glaucescens, A. hallii, A. hyperleuca, A. involucrata, (A. latifolia), A. lemmonii, (A. linaria), A. macrotis, A. nummularia, (A. nyctaginifolia), A. oenotheroides, A. quinquedentata, A. rusbyi, A. scaposa, (A. speciosa), (A. subulata), A. subverticillata, (A. tuberosa) ?? , A. uncialis, A. verticillata, A. viridiflora, A. welshii The names in ( ) are not your plant but A. tuberosa looks very close and may be ?? This info is compiled from the USDA and CalPhoto databases. Here is a link that might be useful: USDA database on Asclepias

It's a Cistus. And yes, it's a shrub. it likes full sun and would be happier without the grass growing through it.

Lantana montevidensis (syn. L. Sellowiana) , trailing Lantana. My advice is that you call your local extension office to find out about this plant's status as invasive in your county. Birds can spread the seeds like crazy.....they are about the only thing for whom the plant isn't toxic.