It's a Spiderwort, botanically known as Tradescantia. Both T. ohiensis and T. virginiana are native to the US. There are several cultivars available also.

The silver groundcover may be Cerastium tomentosum, aka Snow In Summer. Did it bloom with white flowers?

Thanks seedmoney. No, it didn't bloom with any flowers.

Based on the presence of hairs, I don't think this is Tradescantia ohiensis.

Image #3 looks like Lily foliage.

I think it is Tradescantia occidentalis :)

I think it is Tradescantia occidentalis :)

The fruit blossom is plum. The silver ground cover certainly looks like Cerastium tomentosum. The yellow flowers look like Freesias. We don't know where you photographed these plants - that would help.

what is currently the first photo is lily foliage with violet foliage. What is currently the final photo is some type of Alium (onion), which could be edible or not depending on the variety. I am in agreement that your silver foliaged plant is Cerastium.

Are you in Australia? Your tree behind the Hebe looks suspiciously like one of the gold varieties of Melaleuca such as "Revolution Gold' A closer look would help to confirm this.

Thanks, I'm in Melbourne, VIC, Australia :)

Thank you very much everyone. I will get close up shots of the tree and post them soon.

Here's a close up and I've uploaded a few more in the link below. Thanks.

Here is a link that might be useful: Uploaded pics of a few other unidentified plants.

Yes, looks like the Melaleuca 'Revolution Gold'.
I'm in Melb. too. :o) Hi neighbour!

Hello neighbour, thanks for that id! Any idea about the others? I keep discovering something new in my garden popping up every other day!

PS: Do you want some maples? lol

I would love to grow that Maple but alas, no room. :o(

The ground cover amongst your Violets is Wandering Jew...a weed. Can cause skin allergies on dogs. It is hard to get rid of because anything left will grow back. Vigilance is needed.

The garage wall has Ficus pumila, creeping fig. It is pretty and useful but if not kept under strict control, can turn into a monster....you might want to Google information about it before the trouble begins.

The small plant with the shiny leaves is Coprosma. Considered a weed in Melbourne. An untidy bush that is hard to keep to a decent shape and reseeds everywhere. I would pull it out now while it's small.

Sorry to be so negative, just being honest.

Dee.

Thanks for the heads-up on that. I'm going right now and attacking those weeds!

There is so much more that you could learn about your new garden from local sources. I wanted to email you but there is no email address for you. If you want to touch base you can email me at deesrosyview@gmail.com If not just ignore. ;o)

All the best with your new adventure!
Dee

Thanks - you have mail. Have been removing that weed for the past hour!