Answers: Sometimes coolant hoses have a steel coil inside them so they won't collapse. They rust and disappear. Or the rubber could be antiquated and soft. I'd replace the hose.
Your shifting problem may be a 'modulator'. You can get it at a parts store.
If you don't own a puddle underneath but you are losing antifreeze then you could enjoy a blown head gasket or a cracked guide.
Collapsed hose usually means the wet pump is sucking, but the thermostat is stuck. Lower hose usually collapses first, but some lower hoses have a spring inside to prevent that. If yours does, later it will collapse the upper hose.
As for the transmission, it sure would assistance if you told us the make, model, engine, and mileage on your vehicle a bit than makes us guess.
Rick
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