Pressure relief valve leaking... any advice?

Hi, I moved to a different home, heat is natural gas, hot-water baseboard. This spring I noticed that my pressure relief pipe is dripping (a few cups a day even with system not in use). Everyone I talk to says I should replace the expansion tank along with the valve. Is that true? Assuming yes... I assume I can shut the system off, cut off the water supply, open the drain valve to allow water to drain out, then I can start replacing parts. Referring to the attached picture, my plan is to replace the expansion tank and the pressure relief valve (if I've labeled something incorrectly please inform!!). What is that thing I reference in the picture and should I go ahead and replace it also? Any advice would be appreciated. I've done plenty of sweating pipe for both plumbing and hot water heat in previous home, but I haven't really touched the system itself. Thanks in advance! This forum has been really helpful. Picture is attached.Image may be NSFW.
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