To make sure what is going on in your tranny, you need a high level scan tool to check the transmission and tell you what's going on. I think the transmission is on its way out (based on the mileage and symptoms) and does not worth putting serious money it in. I would drive it till it stops working. 

To answer your side question, yes it's limp mode.

The issue seems to be sporadically occurring and then quickly remedying itself.

Even when the computer loses communication with the TCM and then quickly regains communication with the TCM (because the car starts shifting normally again) it isn't throwing any Transmission Codes.

It's throwing a Communication Code (U0101). So it's a CAN Bus issue.  (The CAN Bus voltage signal, which the Computer and TCM use to communicate, sporadically isn't being received by the PCM for some reason)

Could be an internal issue with the TCM, a problem with the wiring from the PCM to the TCM, or the connectors at either component (or between each component)

As soon as the PCM and the TCM can't communicate the transmission defaults to limp mode.

So, you can buy a TCM on ebay, give them your vehicle identification number and they'll pre-program it for you. It will still cost several hundred dollars so you may want to check a few things before you consider it.

If it's a wire/connector issue, the problem (and the code) will persist after you install a new TCM.

So the question is, do you want to "go down fighting" and take the time to watch a few youtubes and learn how to do a few procedures to troubleshoot a few things before buying a new TCM?

You'll want to watch a couple on CAN Bus basics, just to familiarize yourself with how the computer (ECU/PCM) and various control modules (including your TCM) communicate with each other using a Controller Area Network over a twisted pair of wires referred to as a Bus. (CAN Bus). It ain't "rocket science.

You'll be dealing with a computer (TCM) and like all auto computers it has a wiring connector that has dozens of pins on it and without a little bit of background knowledge it's very intimidating.

You'll  also want to watch a couple of youtubes on using a Terminal Pin-fit/Tension tool. Because it's a computer sending/receiving low voltage signals to another computer using male/female connector pins in an environment subject to vibrations, jarring, and climate.  The female pin sockets (on the wire harness connector )  have to fit snugly on the male pins (on the TCM) or else you'll get failure/intermittent failures in communication/connections.

A good place for a warning: Do Not try to shove anything into those female socket pins except the correct gauge tool.

You will create a problem where you didn't have a problem.

You can get a small Terminal pin tension tool set for around $20.

So here's the PCM to TCM CAN Bus circuit on your 2007 Mazda 3. It's a pretty direct circuit from the PCM to the TCM with only one "splice" to another unrelated connector (D-02 Connector).

So, before even "starting", check that TCM connector's wiring harness from the TCM back to the PCM for any damage. It could have a spot where it's been rubbing on metal for 14 years and has finally breached the wrapping/conduit and has damaged a wire. Use a mirror to see places on the bottom of the harness which aren't visible from the top.

The most likely failure point is the wiring connector/socket pins which are attached to your TCM that sits on the top of your vibrating transmission.

So the starting point is to disconnect that connector at the TCM, grab a magnifying glass and inspect the female pins in that harness connector and the male pins on the TCM. You're looking for corrosion, discoloration, and damage to any of the pins in the connector or on the TCM. Look for any pin that looks different from the rest.

You don't have to be an expert because there's no "wiggle room" here. Both the TCM's pins and the Connector's female pins have to be clean and undamaged. Perfect condition. Any "wiggling" at this connection will create a malfunction.

You'll want to lightly push and pull on the 2 CAN Bus wires on the back of the connector to be sure their pins aren't retracting into the plastic connector under pressure. (Like when the connector is pressed onto the TCM)

No obvious issue there? Then it's time to use the Terminal Pin Fit Tension tool to be sure the female pins aren't expanded to a point  (from wear/vibration) where they aren't keeping good contact with the male pins on the TCM.

You don't have to check all of them (you should) just the 2 pins for the CAN Bus will do.

These are the 2 CAN Bus female pins on the wiring connector on your 2007 Mazda 3's TCM  that you really want to concentrate on. (B & E) (also identified in the aforementioned  wiring diagram)

Use the Pin tension tool. If you don't feel a drag on the tool, then you can watch some youtubes on how to replace a single female pin in that socket. (50 cents as opposed to buying an unnecessary TCM).

Lastly, if nothing else seems to be wrong, you can "back pin" the TCM connector and test the signal voltages on the CAN Bus wires. (You probably learned this when watching a CAN Bus basics video).

The problem is, this is an intermittent issue and unless it's occurring when you test the voltages, you won't see a problem.

Hopefully, you'll discover an issue with the wiring/connector/pins (cheap fix)