What's your question? Ask

According to the Arbor Day Foundation, the white pine is the fastest growing pine tree, growing approximately 1 to 3 feet each year before reaching maturity (80 ft.).

Both pine needles and eucalyptus leaves in themselves will not hurt your plants, but both needles and leaves are known to raise the acid levels in the soil they decompose in. This will not cause a problem for your plants as long as you regularly test the soil (which should be done anyway to make sure nutrients are balanced) and treat the soil if the acid levels get too high.

Here is information on treating high acid in soil:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lower-acid-soil.htm

It can drop sap anytime of year, but typically it is worst in spring and fall.

If this happened after it was repotted, it could simply be focusing on growing roots. As long as the plant looks healthy overall, I would not worry about it. It should start to grow again in a few weeks, particularly as the weather warms up.

You can put a splint on it like you would a broken bone and sometimes the bark will heal back. But the splint will always need to remain.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/trees/tgen/what-does-a-dying-tree-look-like-signs-that-a-tree-is-dying.htm