To answer the question in your thread title, sure! Assuming neither the case nor the motherboard are proprietary, you can always put a MicroATX motherboard in a mid or full tower or desktop ATX case. You just cannot, of course, go the other way around.
And the ATX PSU will fit the case and support the board too - assuming the board is not too new and the PSU too old to have the latest connectors (not likely).
So, how do you know if proprietary, I hear you ask? If the case, or the board came from a major factory computer maker, such as Dell, HP, Acer, Lenovo, etc. there is a chance one or the other is proprietary. 
What you need to do is inspect the case. ATX compliant cases are designed to support 1000s of different motherboards. So, it is common for cases to have more motherboard mounting points than boards have mounting holes. And while the ATX Form Factor standard dictates where motherboard mounting holes “can” be on motherboards, it does not dictate where they “will” be. So, one board may have a mounting hole in a specific place while another may not.
A common mistake by the less experienced and distracted pros alike is to insert one or more extra standoff in the case under the motherboard. Any extra standoff creates the potential for an electrical “short” in one or more circuits. The results range from "nothing" (everything works perfectly) to odd "intermittent” problems, to "nothing" (as in nothing works at all ).
So, it is good you are already concerned about standoff placement. You need to inspect the case and note where the mounting points are, Then inspect the board and make certain there is inserted a standoff in the case only where there is a corresponding motherboard mounting hole. If mounting points and mounting holes do match, ensure a standoff is inserted there. This ensures the best grounding but also properly distributes pressure forces - important when connecting connectors, and mounting and using heavy CPU coolers.
Note the primary difference between a MicroATX board and standard (full) ATX board is the length. In a standard tower configuration, starting at the top, both boards will be the same - in terms of possible mounting hole/standoff locations. So with that in mind, working out where the standoffs go should be pretty obvious upon close inspection.
Also, with the motherboard sitting on the standoffs, make sure the motherboard's expansion card slots and rear panel I/O area line up properly (in the height of the board off the backplate of the case) with the rear of the case. If you ensure you only use the standoffs that came with the case, the height should be correct.
If the 4 mounting holes for the PSU align with the 4 mounting points in the case (and they should if both the case and PSU are ATX compliant), you should be good to go there (assuming the PSU has enough power to support your components). Again, if the PSU came out of a factory built computer, it might be proprietary. This can be verified by connecting the PSU simple PSU Tester. Of you can verify the pin-out if handy with a multimeter.
HOWEVER - in the body of your post, your comment does not line up with the title question. You said (my bold underline added),
So are you looking for a microATX motherboard or a standard size (full) ATX motherboard? Again, a standard board will NOT fit in a microATX case. But a microATX board will fit in a standard mid or full tower ATX case (if ATX compliant and not proprietary).
Clear as mud, huh?
