This issue could be caused by a lot of causes.
To start with, it could be a matter of poor data coverage. If you experience the delays at the same time of the day at the same place, maybe that spot isn't that well covered and you just have bad luck receiving messages over there. So if you are always on the same spot, try a different one.
It could also be a connection error. Do you experience the problems when one particular person sends you messages, or with everyone? And do they experience delays too when you send messages to them?
It could be a malfunctioning 3G. Try to turn off 3G (if you can) and just use GPRS. There have been reports iMessages didn't work out well on 3G, but on GPRS it worked like a charm (it doesn't make any sense to turn off and on 3G just to send iMessages, but at least you'll figure out the cause).
And the last, and probably the most unliky cause, could be an issue at the Apple servers. It happens sometimes, when those things get really busy, they protect themselves and spread the work over time. As I said, it's very unlikely, but it happens.
And to answer your second question; yes indeed. If iMessages fails to send, your iPhone will try to send it as an SMS. You can activate this function at 'General < Messages < Send as SMS'
I had something similar. To fix it, go to the Settings app, then General, then scroll down all the way to the bottom and tap Reset.
This gives you various choices, but Reset Network Settings is what you want:
you will then be given a confirmation to Reset Network Settings -- tap the text.
The phone will restart, and your Messages and texts should work fine. You may have to enter your WiFi passwords again, and on my phone, Mobile/Cellular, the toggle for Mobile Data / Cellular Data had been changed, so it may be an idea to check that.
Best Answer
I’m not sure what steps you have taken to resolve the issue so I’ll go least invasive to most invasive.
-Restart your computer -sign out of messages and sign back in -if the issue persists set up a test user account and attempt to replicate the issue. Below is a link on how to do so.
https://support.apple.com/kb/PH25796?locale=en_US
-if the issue replicates in a test user than you have a system wide issue involving the messages app.Next steps would be to make sure your data is backed up and perform an in place install using the recovery partition (hold down command and r on start up and choose install high sierra). Being that your CPU usage is high for this app, install may be the best step.