Number 4 is the big clue. One side of your electric service is dropping out, turning on the stove causes it to back feed. This is likely caused by a loose connection on one of the service lines feeding your house. There are however a few other possibilities I'll cover below.
For the sake of explanation, let's say the location of the problem is a loose lug inside your electric meter. Over time that loose connection has been building up heat, it's likely aluminum wire that melts and burns and produces black carbon. As this continues over time it eventually works its way "open" and will no longer feed that side of your electric service resulting in partial lights out in your house, that might mysteriously just come back on as that burning lug cools down. You turn on the stove (which uses both sides of the electric service) and it back-feeds current through the circuit back to that bad lug, when that happens and the two opposing sides of the electric service meet it arcs and it can actually create a weak "weld" of sorts, restoring the power again, until the connection once again burns open. repeat. Eventually it will just burn open and be broken until someone finds the problem.
Connection points on the power companies side include the pole (or underground connection vault or stump), and the meter can, and possibly an outdoor disconnect. Most often in our area the problem is one of the meter lugs was not tight.
On the customers side, where the service feeders connect to the main breaker inside your panel is also a place for a possible loose lug. (In my area the power utility will actually tighten main lugs in the customers panel, many utilities however will stop at the meter.) Beyond that it's also possible there is a problem with the main breaker or panel buss itself, but that's less likely (IMO) than all the above.
Start with a call to your power company and report "intermittent partial light out". They will check connections outside your house and may even check your panel for loose feeders. They also may not check past the meter, in that case you would need an electrician to check your panel for loose feed--if the power company didn't solve the problem outside.
Most electric utilities don't charge for the service call for their side, if it is your equipment in the end, you will of course have to pay an electrician for their work.
First step is to shut off the breaker for that circuit.
Remove the outlet and GFCI and use wire nuts to make sure the original circuit is complete to the other inside outlets.
Then cover it with a blank plate to make a junction-only box out of it.
Then you are finished with the inside outlets. Turn the breaker back on and use an outlet tester on each one to verify your work.
Highly recommended: Always use an outlet tester to ensure that the wiring is correct for each outlet. It can detect all sorts of faults and, even better, it can confirm that you have done the work correctly.
This is a great tool to have around when doing any kind of electrical work, and they are inexpensive. Might not hurt to use one to check all the outlets in your home.
Here is an example: Home Depot Outlet Tester
(Aside: I snipped this image from the Home Depot website, and it appears to be indicating an open ground - just the center light is lit. On the top of it is a chart showing how to interpret the light patterns.)
Install another outlet box against a stud for the GFCI.
In that box you will prepare your connections to the GFCI.
GFCIs have an input side that will come from the breaker, and they provide output terminals for connection of additional outlets.
From the breaker box, feed Romex down to your crawlspace.
SAFETY FIRST - DE-ENERGIZE THE BREAKER BOX WHILE DOING THIS
Feed it down then up to the GFCI. Attach the Romex Ground, Neutral and Hot leads to the input side of the GFCI but leave the GFCI hanging out slightly so you can attach the outlet string to it..
Cut off the Romex at the breaker box with a little excess and tie it off - it is not yet time to connect the new breaker.
You can then re-energize the box while you work on the GFCI and outlets.
From the output side of the GFCI you will run Romex to other outlets. Use a mounting box for each.
You can go laterally to the outlets - just drill a hole in the middle of the studs for the cable to pass through - there is no requirement to use the crawlspace for them. That might be easier than making new penetrations to the crawlspace for each outlet. Totally your choice.
Each outlet has 4 connections plus ground: one pair for input then the other for output. Use that to daisy-chain multiple outlets in a string.
Make sure you include ground in the daisy-chaining.
By doing it this way they all will be protected against ground faults, and all of the garage outlets will be on the new circuit.
To finish up, screw in the GFCI and the outlets into the boxes then put on nice attractive cover plates
In the crawlspace, secure the Romex to your floor beams or wherever with something like this:
Last step: Make your supply connection to Ground, Neutral and the new breaker inside the breaker box.
SAFETY FIRST - DE-ENERGIZE THE BOX WHILE DOING THIS
Pull the Romex up tight and cut off the excess, strip the ends and do the final connections.
It helps to leave a little extra length to make the work easier. I sometimes add a small loop of Romex inside breaker boxes, depending on how full they are.
Make sure all connections are secure and that there is no mechanical stress on the cable.
When finished, put the metal cover back on the breaker box, re-energize it and use the outlet tester to verify power (and proper wiring) to each outlet.
Test the GFCI with the outlet tester plugged into one of the other outlets.
Voila, a whole new 15 Amp circuit in the garage, all protected via the GFCI.
Best Answer
I would feel somewhat more comfortable if you had found three hot cables, and each cablewas turned off by a different breaker. As things are now, you have not, and you must be careful that you do not accidentally connect two breakers nose to nose, feeding power in one breaker and out another. That will either create a loud flash-bang, or seem to work but then create a lurking safety hazard that can start a fire.
I would expect that one of your four "dead" ones is in fact live, and something has gone wrong with your testing method.
I am fond of dollar store nightlights and cheapie extension cords. I cut off the plug (part with the blades) and throw it in the trash. Then, I take the rest of the cord and split the wires and strip each wire 3/4". Then I wire-nut it onto a hot and neutral I aim to test, and plug in a nightlight or a radio, then see if I can energize the circuit.
Anyway, 3 breakers, 6 cables, makes sense. 3 of them would be supply side from the breaker (possibly stopping at intermediate points first) and 3 would be onward power from each of those circuits. I would identify every one of your 3 supply lines, as best you can, using the extension cord trick rather than a non-contact tester.
Also for each of the 3 circuits, figure out what sockets or fixed loads each bris powering now. The ultimate goal is to identify all the loads connected to each of the six sections of cable.
Now, turn off all of the three breakers but one. Run a cable from the hot wire over to one of the 3?4? mystery sub-circuits. Then search the house and find out which sockets or loads that circuit powers up. Mark accordingly.
Once you have mapped them, there will probably be some logic to how they are wired and how to match them up.