To me the first photo looks like liriropi and the last one oleander. The plant in the second photo might be Texas sage. I hope someone else can ID the others. Maybe a closer look at the leaves would help. Wishing you the best in your new garden!

I hope that you love your new home!

I think that the 4th picture is some sort of salvia. In picture 5, I see an amaryllis toward the left front and salvia ( I think) on the right. No clue on the tall plant. I agree with Roselee's IDs on the others. Picture 3 looks familiar, but I just can't think of the name.

Thanks a lot!! Really REALLY helpful :)

What part of Texas do you live in? I agree that PKPonder and Roselee got the IDs right and the third one does seem familiar. The leaves sort of look like Weigela, something I haven't been able to keep alive in far NW Austin.

Definitely agree with liriope and oleabder I am not sure the 2nd one is texas sage but maybe. Its hard to get a sense of how big the leaves are. Agree azalea is possible for the next. That might explain why it is yellow, because they are hard to grow in most of texas, with the eastern part of the state being the exception. I wouldn't tear up the garden yet, with the exception of the azalea maybe, You might have some perennials in there

Closer views needed, more of last one needs to be seen. Yellow one is not an azalea.

Third is Azelea. They can look like that when they have chlorosis. They need iron fertilizer.

#1 is Liriope and I would definitely keep them. They make such a beautiful border with no effort. They get pretty purple spikes for a few weeks in the summer too!

The last one is definitely Oleander. That's a great plant for all summer long blooms.

The second picture could it be a shrubby Germander Teucrium fructicans. Some are glaucous and other varieties are greener ,. a grey green. Also it could be a glaucous one that is in a bit of shade that might make it greener and less blue. Click on the name and it will take you to growing conditions and peoples opinions.

The foliage of Germander teucrium fructicans is said to be aromatic so that may be a determining factor. I've never grown it, but am thinking I should.