Some research led to this article from AllThingsD about how an Apple rep had confirmed that the service does indeed stream the music, but it also saves to the device, thus taking up storage space. It starts playing before it finishes downloading, but it does actually download and save.
MacRumors and a video from InsanelyGreatMac are somewhat unclear about this, but MacWorld agrees that on an iOS device, it's downloading (scroll down to "Playing iTunes Match songs on your Mac and on iOS").
UPDATE as per comment:
As of iOS 5, the device will delete cached data from apps when it's low on space. This caused some controversy at first because apps had no way to prevent cached data from being removed automatically. In the linked article, Marco Arment provides an example:
A common scenario: an Instapaper customer is stocking up an iPad for a
long flight. She syncs a bunch of movies and podcasts, downloads some
magazines, and buys a few new games, leaving very little free space.
Right before boarding, she remembers to download the newest issue of
The Economist. (I think highly of my customers.) This causes free
space to fall below the threshold that triggers the cleaner, which —
in the background, unbeknownst to her — deletes everything that was
saved in Instapaper. Later in the flight, with no internet
connectivity, she goes to launch Instapaper and finds it completely
empty.
This was fixed in iOS 5.0.1 (Apple Developer documentation) so that developers can differentiate between cached data that is and isn't important.
So, the short version: Once free space gets below a certain level, the device will regain whatever space it can by removing cached data from installed apps. If it can't do that, or if you're completely out of space, it'll probably just tell you that you don't have enough space to do what you're trying to do.
Each account can only be set to one region. According to the knowledgebase article below, one should be able to change the region on an account. Since this process doesn't seem to have worked properly in your case, I'd suggest contacting iTunes support.
http://support.apple.com/kb/ht1311
However, you could have two iTunes accounts; a UK account and an Irish account. The advantage here is that you don't have to worry about a previous UK purchase not being available in the Irish store.
To get an iTunes account in a country in which you do not reside (and therefore do not have an address or credit card from that country), you could purchase an iTunes gift card from the country in question and follow the instructions in the
How to redeem an iTunes Gift Card on a computer > I do not have an iTunes Store account
section of the following knowledgebase article:
http://support.apple.com/kb/ht1574
You will need to authorize both accounts in the Store menu in iTunes. Once both accounts are authorized, you should be able to update the apps you purchased with your UK account as well as any new apps you purchase with your Irish account.
On your iOS devices, however, you can only be logged in to one iTunes account at a time (Settings app > Store > Apple ID). On the device, over the air, you can only update the apps associated with the currently logged in account.
I hope this is helpful.
Best Answer
Without knowing the actual apps you're trying to install and what version of iOS you're running on your iPhone 4S, any answer you get is likely to be at best an educated guess.
There are a number of possibilities for your situation, but my first thought is that although you say nothing has changed on your Mac or iPhone, that doesn't mean something else hasn't changed.
Specifically, what I'm thinking is that many software developers are busy updating apps at present due to a number of updates (e.g. iOS 10, Xcode 8.1, Swift 3, etc). In doing so, many apps may become incompatible with older hardware and/or operating systems.
In your case you've downloaded the apps on your Mac, so there's no built in check going on as to compatibility. What I mean by this is that browsing/downloading the apps via the App Store on your iPhone will only allow you to download versions of apps that will install on your device, but there's no way for this to happen via the Mac as you could be downloading them for any number of devices.
Another factor is that your model of iPhone cannot run a version of iOS later than 9.3.5, so any apps requiring a more recent version will not install (and that's assuming you're even running iOS 9 (many iPhone 4S owners aren't).
You'd be best to use your iPhone to download apps as many developers (me included) do allow older versions of their apps to remain on the App Store for superseded devices etc.
Hope this helps!