Those black pieces are meant to turn 360 degrees in any direction. You already have a key to turn them, in the form of a fluorescent tube. Keep the tube as close as possible to its proper position (i.e. don't try to do this at much of an angle). Turn off fixture power.
Worse come to worst, if you break the lampholder (aka tombstone) or if that type just annoys you (they annoy me), new lampholders are fairly standard, common and cheap. I typically pay 60 cents each for them and keep a bagful on hand. You can mix and match types though I prefer to keep "circular" types separate from "v" types. Height is also a factor, they come in 3 heights. Yours looks like a medium. You don't want a short but a long will probably suffice.
The $3000 cleanup was never a thing. It's an urban myth created from a political slander. The goal of the slander was to resist CFLs at any cost, both to resist government regulation generally, and efficiency due to its association with climate change. This also tied into 50 years of activism to reduce mercury in the environment. The fact is, if the mercury in a broken CFL were any danger, or any problem in the waste stream, they would never have gotten government or UL approval in the first place.
So this was not a surprise; the mercury "problem" was contemplated and resolved long before it became a spiral shaped political football. EPA and various state DEQ's have collectively rolled their eyes and said "allriiiight... Since you insisted on bringing this up, here are some best practices for cleaning up a CFL" and they involve stuff like mopping it up with the sticky side of duct tape.
You would be best following that advice.
(if you called enough remediation companies, eventually someone would take your $3000, but don't.)
If CFL recycling facilities exist at a nearby city or big box store, use them.
Otherwise just put it in the normal waste stream, not commingled or encased with recyclables. Don't put in a steel can. You may not be aware of it, but they don't just tip the truck at the dump anymore, now it goes through a complicated screening to find recyclables. Some of it is automatic (magnets to pull out steel, magnetic-field tricks to flip out nonferrous metals etc.) and and hand inspection for bundles of newspaper and the like.
Using a steel can as a jacket for something nasty will only get the nasty thing into the steel recycling stream.
Best Answer
The bottom two are bi-pin fluorescent tubes. There are two types of bi-pin socket you will encounter on straight tube T5, T8 and T12 fluorescent lights.
This type requires 90 degree rotation.
Removal can be a real pain the first time you do it as the pins can weld to the brass contacts and you will end up breaking the socket if you get rough with them. I use silicone spray with a straw to shoot some into the socket when I encounter one that's semi-spotwelded itself in. It's non-conductive and prevents future issues. Rotate the tube 90 degrees so they align with the slot and pull out. Also, if the tube is too long to allow it to drop out of the fixture opening, there often will be a slot in one end to drop the pins into so the other end will clear the opening.
Align the pins vertical, insert the tube until it stops and rotate until you feel both pins click in place, it is possible to have only one set engage in the indent in the brass contacts that are visible.
This type pushes straight into the socket and removal is straightforward.
The top two tubes in that picture are compact fluorescent and pull straight out of the socket.