What pipe is this

Did the problem just start? Is the condensation on the pipe frozen? If so, this is an indication that the compressor is overworked (possibly low on coolant). If you are seeing any frost, you should turn off the system before the compressor burns out and call an HVAC professional.

Insulation is wrapped around the coolant line to prevent condensation from forming and causing damage. That insulation may have started to fail. If so, replacing it is an easy enough job.

I reccomend you turn off the system for a little while so the coolant line can warm up. Pull off as much of the old insulation as you can and wipe it down to remove any leftover condensation. Then replace it with the tightest-fitting and highest R-value insulation you can find.

When re-insulating, be sure to seal all of of the crevices. If the pipe insulation tubes have an open slit in the side, make sure you seal the slits with insulated tape. If any copper is exposed, it is a point for condensation to form. The coolant line should be completely covered from end to end.

I reccomend that you don't bend the pipe. The coolant pressure is somewhat higher than your generic water supply, and if you damage/crack the line, it won't be pretty.

1. A water expansion tank gives water a place to expand in a closed system (frequently found with boilers, or home water supplies with a check valve). Otherwise, heated water cannot expand and instead increases pressure until some component of the system leaks or explodes.

2. If the tank is on the hot water heating system, then it's there to relieve expansion from the water being heated. I can't tell from the photo if it's on the heating system or on the home water supply.

3. Leaks tend to travel down with gravity, if you see evidence of a leak above the tank, then it's likely at the top of that evidence, not the bottom. Shutoff the water, find the source of the leak, and replace the problem area. It may be as simple as needing to unscrew a threaded connection, clean the threads and apply pipe dope, then tighten everything back up. But with visible damage, you'll likely need to to replace the problem area with new pipes.