Please help- Mystery plant & garden advice needed

[FranklySonImTheGaffer]

Hi all 👋

We have just had a giant conifer cut down in the garden and are now considering what to do with the space.

There's a bush growing in the corner with white flowers (pic 1). Can anyone ID this please? I don't want to cut it down, it's pretty and attracts lots of bees but I need to know how to prune it / keep it under control (it's roughly 3ft tall now).

I also have 2 big wooden planters and am considering using those instead of planting into the ground (the soil is clay heavy and a bit rubbish).
Would lavender be ok in a pot? The only other thing I can think of is a herb of some kind - rosemary? Mint? I'm completely clueless so it needs to be minimal maintenance!

Last question - the only think I've ever kept alive so far had been a cactus so I've adopted one DH was given. I'm going to repot it but had left it with some water and sunny spot to check it was still alive - it's grown a really long stalk type thing (pic 2). I'm confused - is that normal? Should I cut it? My original cactus has grown offshoots but they look the same as the 'main body' so I've never given it any thought.

Please please help, I have no idea what I'm doing!

It's a Hebe - bees love them.

Thank you both so much!
I will google a Hebe now. It's really pretty, it's just that it's against a fence at the front of my house so I need to make sure it doesn't push to much against the fence or get too tall.

The 'cactus' was a teacher present for DH. He abandoned it for a few months so I thought it was dead. As long as it doesn't need too much care I'll give it a go.

Mint is a definite for at least one planter then, my grandad used to have some and I loved the smell..

There are loads of things you can grow in planters. Are yours in sun or shade?

Mint is generally recommended for planters because it's such a thug otherwise, spreads everywhere given a chance.

I've got lavender growing well in a pot, it does need pruning to stop it getting woody and leggy. All my other herbs are in pots too (rosemary, sage, thymes, oregano, chives) partly so I can have them next to the kitchen door but also because I have a dog....
So a planter of herbs is definitely an option, they mostly like full sun.

Clay soils can be very good for growing stuff too.

The "cactus" isn't an Aloe but a Haworthia - succulent plant. It appears to be planted in a glass bowl with no drainage holes, which it won't like much - these plants need excellent drainage. It would be much happier in a proper pot with drainage holes and a gritty potting mix, otherwise it is quite an easy plant to grow.

Thank you for your help, I was complete at a loss earlier today!

So I think for the planters I'm going to attempt lavender, mint, rosemary and sage.
And as for the cactus / aloe / Haworthia, I'll repot it into a pot with drainage and do a bit of googling.

And the Hebe is going to be left alone , maybe trimmed / dead headed every so often but that's about it.

Useful rule of thumb, if you don't know what a particular plant is, is to prune it just after flowering (unless it flowers late in the year, when you might want to prune it in early spring instead). Doesn't apply if the plant produced berries that you want to keep (Hebe doesn't).

If you want to drastically reduce size, it's often best to selectively remove whole branches (targetting the older ones) rather than giving it an overall hair cut. Don't remove more than 1/4 - 1/3 growth in a year - stage major cutting back over 3-4 years.