Update

So long as the ground is workable, and you can dig a hole for it, yes you can plant them now. Add a layer of mulch over the top to moderate the temperature and allow it to root in quicker.

If they are in pots they can be planted at any time the weather is suitable but personally I wouldn't plant a Pittosporum that large in winter as they can be a bit tender and you didn't put your county on your profile..
Smaller shrubs tend to establish more quickly than larger ones and soon catch up.
Not sure what you mean by a dwarf palm as there are several plants that look like palms but aren't. Have you got the name of it?

Yes, the 'dwarf palm' caught my eye too - there's only one fully hardy palm that grows in the UK, which is Trachycarpus, but its certainly not a dwarf. Cordyline (common name cabbage palm) can survive here, but when they're small, they may not make it through a winter.

If you research Trachycarpus wagnerianus (the dwarf chusan palm) - you will see that it is hardier than the regular, larger Trachycarpus fortunei.

Cordylines don't stay dwarf though do they - will look like a palm tree when they mature.

That fan palm in your photo won't be hardy. The attractive one recommended by Longleaf should be, but it will eventually grow to 6m tall and you'd have to order it on line.More info needed if you want plants you don't want to spend much time on. Do you need them to be evergreen and how big do you want them - do you have a height limit? What sort of situation are they for - a narrow or wide bed, near a wall or house or in the open, sun or shade, windy or sheltered?

You may not find the best options or advice in a DIY supermarket if you don't know much about what you're buying. Its so disappointing if you plant things that look nice now but in a few years don't do what you expect.

Well, climate change is clearly advancing - I just looked up Chaemerops humilis with the RHS, and its now listed as hardy throughout much of the UK, although I'm sure in colder, wetter regions, its likely to look pretty tatty after winter. I've certainly seen it growing very well on the coast up in Norfolk, despite all the cold winds, but then the coast is always warmer than inland and Norfolk is a low rainfall area. However, its not a good idea to plant it now - best wait till mid spring next year, keeping it watered throughout summer, so it has a chance to get established before it has to face a winter. Same goes for Pittosporum and, in case you were thinking of planting one, Ceanothus varieties - they're best planted in spring, just in case we have a hard winter, or you live in a cold region of the UK.

Good luck with the palm then - hope it does well as its very attractive. All our answers do depend on size and location though so more info would still be good.