1 Lucky Texan

DOH, beat out while typing you can sometimes find FSMs on line - do a search and include ' .pdf ' in the string.

I'd think you'd return to the dealership and have them fix the car - if they balk - contact SOA and meet with a regional rep at the dealership.

most folks avoid Bosch - Denso I think is OEM

yeah, live data or freezeframe data might be good here - fuel trims may be 'off' , or temp sensor bad, ,,,knock sensors can be cracked and will kill power , good suggestions above.

rear O2 could be bad, exhaust leaks will cause that code - just be SURE before spending $$$ for a cat.

I'll suggest Valvoline MaxLife (Dex III/VI w'ever) for the 4EAT. a lot of the fluid stays in the torque conv. 3 drain and fills with a little driving between gets you over 80% new fluid - there are ways to do a complete swap of course, search for those ideas. If you are having any delayed engagement, a bottle of Trans-X on the last fill really does refresh seals. Sneak up on the hot (operating temp) full line - the marks are only a few ounces apart. Run thru each gear and check while idling of course. The Subaru new OEM ATF-HP may be a little better for you with extreme cold..... not sure. It is a thinner viscosity and a 'must' for the 5EAT in 05s - up. consider using a turkey baster with a short hose and refresh power steering fluid with some new ATF too. name brand GL-5 should be fine for the diffs, synthetic might be best in your harsh climate. You might look for the synthetic 'blend' at WalMart - inexpensive and some folks seem to like it. take the FILL plug out first on the rear diff, that way, you know you can get fluid into it. If you drain, then can't bust the fill loose, can't drive the car! I used my floor jack on the handle of my breaker bar. Those things were TIGHT. I used these items to help with the rear diff and the trans/front diff;

find an independent shop to diagnose the car. P0420 is rarely a bad cat. conv. Some scary sounds are a weak timing belt tensioner and not rod knock or piston slap, etc. check you local Yelp and Angie's List, check your 'region' at www.NASIOC.com

some folks have had a weak timing belt tensioner mimic rod knock. there's a youtube video or 2 about it.

how many miles on the trans? you might find a much lower miles entire trans from car-part.com or ???? to swap in. I THINK there is a certain year where some internal part was changed to a better alloy too???

Im with nipper, I doubt it can truly be 'rejuvenated'. some folks like Aerospace 303 protectant - but probably short term too

some cars with bad plug wires or coil, or, maybe with oil leaking onto the plug boots, will drive-off moisture when temps increase, reducing misfires. Some folks have even used plant mister bottles undehood at night on their idling car - the mist will show arcing and maybe cause engine stumbling. The other issue could be as I oultined above about the engine temp sensor - if the ECU thinks the car is always at a higher temp, it won't 'choke' by sending more fuel to the injectors when cold. plenty of other things other things; like a gummy deposit in the throttle body or gummy buildup in the IACV or ???? might be different viscosities at higher temps. Metal parts change shape with temp, wires/connectors/ground connections could change a little with temp. I have read of older crank position sensors that failed at high temp......who knows?

re-read the post, the backfiring kinda points to some timing or maybe valve issue - I suppose over-fueling might be an issue too but???? find the tooth count for the engine on-line. Bring the marks on the pulleys around to the timing points and do a tooth count. here's some wild ideas; one thing that will kill power often with no code is a bad knock sensor, easy cheap to replace too. although it seems to be a rare failure, the car has 2 temp sensors, the gauge part can be good, but the ECU uses a different sensor (in a single unit on some cars) to determine if a 'choke' condition is required and if bad, might not be supplying enough fuel when cold? or too much when warm? another easy thing that will mess with idling - the IACV tube under the intake tubing could be cracked/loose. dirty throttle body might cause idling problems.

interesting - I wonder if a garden-type pump sprayer can survive any useful solvents? also, I found these vids;

there's at least 1 video showing dropped guides. I think a car has to have been quite neglected to have that happen though.

yep - def check timing. I wouldn't rule-out a 'dropped' valve guide or burned valve.

smell it - diff lube is distinctly foul compared to engine oil - you can confirm that by smelling the 2 dipsticks.

Subaru Coolant Conditioner has helped folks with coolant drips/seeping. Install ONLY one bottle and ONLY as directed.

every time or first start of the day? CEL on? scan for pending code anyway. fuel pump? Try cycling the key to ON, but without turning-thru to start - still have noise?

typical parts store rebuilts are often wrongly stocked/buoilt for the 3.0 motors. Sure you are getting proper alts? I'm CERTAINLY no expert, but the 3.0 unit may have higher impedance on the 'field' input wire and those (possibly) incorrect alts are sinking too much current from the ECU's control output. Might be worth trying a used alt or, if you still have your original, have a local rebuilder go thru it for you. there's also DBW or maniac electric or ???

check post 15 here; https://www.subaruoutback.org/forums/66-problems-maintenance/34827-automatic-gearbox-fault.html kinda seems like the final 3 digits are for ordering parts - some build details internally ?

so many folks have fixed whining or notchy-feeling power steering with just an o-ring I have read of people modifying Jeep or Chrysler wiper bushings - or the replacement bushing kit parts, and epoxying them into their wiper linkages. Or, they get a new wiper linkage.

^^^^^^such a good post get an OEM spin on filter. be sure the air/oil separator plate on the back of the engine isn't seeping too.

front and rear final drives must match. Some folks swap in rear diffs with a new trans of different FD. But best to find direct replacement of course. checked car-part.com? LKQ? maybe try ebay local pick-up and craigslist in case someone is parting-out.

do tight circles on a paved lot - feel for any binding/jerking - could be torque bind, if 5 spd trans, do this after the car is fully warmed-up. do highway entrances at full throttle as well as exits with max engine braking - watch the temp gauge.

in the past, you could get a cap from an 05 filter kit (throw the filter away), and a 928 metric o-ring for under $75 or so - be sure to inspect any used fuel pump's cap closely - new o-ring would be a good idea too. check; https://www.amazon.com/Genuine-Subaru-42072AE00A-Fuel-Filter/dp/B00L2OWO2U/ref=sr_1_6?ie=UTF8&qid=1538484308&sr=8-6&keywords=2005+subaru+fuel+filter there's a 'dimple' on one of the cap's tabs that I guess is intended to be a stop - don't overtighten and force the dimple over the edge of the plastic lug it's on.