To be honest, we do not know. I've only seen it before at the nursery where it was purchased from, and they really didn't know the name either. I believe it's a type of agave, although some suggest a cordyline.

I think the large plant may be a Furcrea (sp?). I have several in my garden in San Diego. Furcreas look like they'd have sharp spikes on the ends of the leaves but they're actually sort of soft & flexible, & are safe near a pool.

They look like Australian native plants. The large-leaf one looks like a Gymea Lily. It gets one very large red flower on one very very tall stem, each year. Quite beautiful. The red flowering spidery one is Kangaroo Paw, and the ground cover is called Pig Face; it gets covered in tiny flowers - some are pink, others are orange. This grows on sanddunes and over rocks very well - in poor soil in other words, and is a succulent. It is used a lot in Australia to stabilise sand dunes.

What is the name of the small cacti in front bottom of the agava plant??

looks like agave "Blue Glow"