Learning to clean carburetor

Hello all, I'm new to this forum. I've spent the season over at snowblower forum, and this is my first year playing with and learning about small engines. Now that I've been learning, I figured I'd try doing some basic stuff on my Craftsman lawn mower (model # 917376395, B&S engine 126T02-1443-B1). I've had it maybe 2 years but never changed the oil or spark plug, drained the fuel, or cleaned the carb (I know, shame on me, but I'm trying to redeem myself now).



So this year after putting the snowblower to sleep, I drained the old gas on the lawnmower, replaced with Sta-bil-ized fuel, and changed the oil with new 5W30. Before all this, the lawn mower would start/stop two or three times or so, before finally starting and staying running. I figured what the heck, I might as well try to learn how to take apart and clean the carb (I am in no way a mechanically inclined person, but I do have YouTube!).



I took the carb out last night and ran wire through and sprayed carb cleaner through every hole I saw. I did not follow with compressed air or let it soak due to limited time. I was more interested in just learning how to take it apart and put it back together. This morning I ran the lawnmower again (~ 30 degrees outside) and it still exhibits some symptoms of starting briefly and then stopping a couple times, before finally staying running. The lawnmower has an auto-choke mechanism, so I have no idea if the carb still is a little dirty or if it's just a matter of being cold.



A couple questions:



I got some Gumout carb/choke cleaner on the carb bowl gasket. I didn't soak it but some of the runoff spray did come in contact with it. Probably a bad idea right? It seems a little more stretched than before.



What about the needle seat? I didn't have a carb tool handy to pull it out so I just ran a fine wire through it and then sprayed carb cleaner through it. Would carb cleaner damage the seat?



I am considering taking the carburetor out and apart again, and then soaking the parts in Pine Sol. Other than the bowl gasket, is there any part I should take out and not soak? Like the needle seat?



Finally, for those that have soaked carbs in Pine Sol, do you use 100% Pine Sol or do you tend to dilute it with water? And how long do you soak?



Also, although the start and immediately stopping symptom seems to be primarily a carb related issue, can this also occur with a fouled spark plug? I ordered a new one anyways, but I was just curious.



Thanks in advance. As you can tell, I have a lot to learn!