Cutting through ice tips

Finally got my first Beaver last weekend. Biggest challenge has been punching through ice.
Ice was close to 20 inches and have a 20 inch blade on chainsaw. Troubles have been when minus 30, like New Years, as soon as I stop saw, the bar froze so would have to keep stopping to head back to cabin so it could thaw. Moderately cold the pull cord started to have trouble retracting. When had bar oil, an oil slick would be left on surface water but last weekend without bar oil the teeth got majorly dull fast. Switched to ice auger to punch 6 holes side by side to make hole (2 rows of 3 holes all touching), but if near a feed pile, could only get down till chewing branches. February will only get harder.
Questions:
Is it better to use bar oil or not in the chainsaw for ice cutting?
Where can I buy ice or log tongs to help lift out the blocks of ice?
Does throwing snow and pine branches over the holes really help to cut back in for the follow up visits?
What is the most common method to punch through ice (less than 20 inch and when more than 20 inch), initial cut and follow up cut when extra cold?

I used to use a chainsaw with a 24" bar (used to run vegetable oil in it. If really cold, I carried an old thermos with alcohol/water mix to pour on clutch and drive sprocket to keep the saw from freezing solid. Made sure I dry ran the saw after each cut to get rid of as much water as possible and to fill the bar notch with oil before turning it off) but now use a 8" power auger 95% of the time. A heck of a lot easier, you stay drier, and you don't have to worry about the saw freezing up. For snaring - just punch two holes almost touching side by side, then easily spud out middle bridge. This is wide enough to put down a poplar bait pole with 8" snares on either side. Don't drill so close to the feed pile. I plug mine about 3 feet out from where I see the last surface branches on the pile. I check my sets every 1-2 days, so I don't bother covering the top. I find it makes it easier to check without having pulling up the pole. Almost guaranteed you have a beaver if you have large bubbles frozen in the ice. All I do is carefully chip a 2 " hole open, then shine a mini Mag lite down the hole. If I see locks tight to the pole, then I know nothing touched it. Saves a lot of time not having to cut and remove the poles to check. If I can't see the locks, then I pull the pole to check and reset. An ice spud, or an axe is all I ever use to re-open a hole to check. I carry an ice fishing spoon to clean the slush and ice chips out of the hole, otherwise the floating stuff will trigger your snares when you're trying to put the bait pole back down. Make sure you always run a 14ga safety wire!

all I ever use is an axe and a ice chisel works for me