Instead of creating a temp contact just ask Google to make the call. Something like, "hey Google"... "Dial four five six five five five eight seven four two".
In the meantime I'm late to the party so forgive me if I repeat something.
It sounds like you are able to open the app and it doesn't close on you or disappear. That's good.
The issue comes in when you attempt to dial, and this is where I get a little confused. You say that contacts are opened when you press the keypad. Do you mean that if you press a number on the keypad, as if starting to dial a number, the screen changes and opens contacts? Do you mean that you're pressing a 10 dot symbol for the dial pad but instead of opening the 10 digit touch pad it opens contacts, as if the wrong button was pressed? Do you mean that when you begin touching the numbers it begins trying to predict whom you want to call and offers you suggestions from your contacts?
Are you able to finish inputting the number if you just continue and don't get distracted by whatever is on screen? Does the number pad disappear when "the contacts open" or could you continue if you just kept touching numbers?
Are you using the stock dialer? Have you tried another dialer? There are tons of "dialer" "phone" "number pad" apps, whatever you want to call them, at the Play Store. Pick-up one and see if your issue still exists.
You mention turning the Phone app off and on, do you mean closing the app and opening it again or does your phone app some kind of kill switch built in where it's off and... then what? It opens but won't make calls, it opens but has limited options? This one confuses me too, but you don't answer the question of whether or not you cleared the app cache or app data. Did you clear either of them or both of them? I would suggest clearing both. There's nothing for your dialer to log in to and it is associated with the phone so clearing the data should have no ill effect.
If the phone is busy, not a busy signal like back in the day, busy as in some other app is controlling it and preventing you from being able to use it, you can take phone permission away from other apps. This isn't a permanent change, apps needing this permission will ask for it the next time they run or the next time it is needed and then you make the choice just like the first time. Go into Settings and use the search option to search for "permission manager", scroll to the Phone permission, not call log, and remove all apps that can be removed from this permission. Then test if the issue still exists.
Let us know what you find.
Edit: You can also remove the phone app from being the default for another app. This kind of goes with removing the permission. If it is set as the default for some app that isn't closing or acting right it be being kept busy when you're trying to use it. To do this go to Settings>Applications>Phone (there may be more than one app named phone but this is ok to do to all of them)>Set as Default>remove any apps found here. Just like with permissions the next time that app runs it may ask to be the default again.
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