garden question

I have lived in an apartment for almost 10 years, and prior to that, had never gardened in my life. Now we are proud owners of a gorgeous garden, the kind that makes you want to host tea parties with ladies in frocks and matching tea sets, the kind of garden with a deck, gazebo, jasmine covered archways and cherry blossom tree blooming pink in its middle. The ex-owner of this house must've been a great gardener, and an incrediblyΒ thoughtful one. Every couple of weeks, shoots of new, brilliant flowers appear as if from nowhere, and then due to her impeccable planting timing, as they wither, new, different blooms sprout in their place. Our gardens, front and back, are a sea of color, bee activity, and gorgeous scents. It's the most idyllic part of our home, and though I'd never though I would say this, fast becoming my favourite area for working in.

I will need help though. I have literally zero knowledge about gardens, and my skills don't go far beyond re-potting plants. And I don't want to be writing a post in 12 months about how I've killed my garden. So here it starts, a series of garden questions for the hive mind.

This one's first. I love this - its blooms last so long in a vase on my kitchen counter, they're so brilliantly coloured, they grow so quickly!

unknown garden plant!

What I need to know:

1. What is it? (Please don't tell me it's a weed!)

2. How do I care for it? It seems like a creeper of some sort.

3. Do I need to replant it or is it forever going to be there?