There are several ways to get armour pieces and/or frames.
From Exploration
Many of the power armour frames you will find will have randomly spawned pieces on them, and many will be incomplete. According to Fallout wiki, random spawns will be based on level: T-45 power armor pieces at level 1-17, T-51 power armor pieces at 18-30, T-60 power armor pieces at 24, and X-01 power armor pieces at level 26 or more.
There are a number of maps online (IGN, Fallout4map.com) which show the location of all the power armour frames in the game (both random and pre-set) among other things.
From Enemies
You will also find enemies wearing power armour (many of whom are pre-set). These enemies will not drop an armour frame but you can take the pieces off their corpse.
As mentioned in another answer you can take the frame if you make them exit the armour by getting behind them and targetting the fusion core in combat (or reportedly pickpocketing the fusion core before combat). Though apparently if you make an NPC get out of it's frame it will count as "stealing" every time you use it.
From Vendors
If you join the Brotherhood of Steel you will be able to buy T-60 pieces and a frame from Proctor Teagan on The Prydwen (not sure if or how often he re-stocks, but he does restock).
Rowdy at Atom Cats garage will also sell individual pieces of T-45, T-51 and T-60 power armour and a frame (they also have some frames of T-60 standing around you could steal).
You can also buy an empty power armour frame from Commonwealth Weaponry in Diamond City and KL-E-0 in Goodneighbor (if you buy a frame it spawns on the nearby Power Armour service frame).
So Many Frames...
What to do with the spare frames is up to you, they appear to be indestructible, some people have suggested leaving them in lakes or something if you don't want to see them.
Repairing
Yes, broken pieces will be placed in your inventory, and can be repaired and placed back on a frame.
In my experience if you plant something near the bugged plant, assign a settler to that plant, and let the farming run its course, these issues tend to resolve themselves over time.
I've had invasions occur ON my farm plots, and have watched my missile turrets decimate the farm plots, and then not be able to select the destroyed crops.. Poor farm/defense layout aside, this is the circumstance in which I came back later and notice that the plants were eventually revived.
In short, I wouldn't worry so much about micro-managing the efficiency of every single plant. If food and water is sufficient for stability or growth, that's good enough for me!
Best Answer
You won't lose the bonus once you find them, but you will miss out on the awesome opportunity to display them in your home, also its way easier to keep track of which bobblehead you've found already if you still have them.
You can build a magazine rack (2 kinds actually) and bobblehead display station if you have the materials that are especially designed to hold those items.