The largest LEGO set by piece count is :
75192-1: Millennium Falcon (2017)
Piece count: 7541
Second: 71043-1: Hogwarts Castle (2018)
Piece count: 6020
Set 10189-1 - Taj Mahal (2008) (re-released as 10256-1 Taj Mahal (2016))
piece count : 5922
Largest Techic set :
42100-1: Liebherr R 9800 (2019)
Piece count : 4108
If you mean specifically Lego bricks, I'm pretty sure the 1x16 was/is the longest one made. Outside of the 1x? sized bricks, the longest plain shaped brick that I know of is part #30072 or #47122 at 24 studs long. I don't know about other brands though.
Interesting related post:
What is the largest single LEGO piece?
I think it's going to be the 1x12 (#60479) and 2x16 (#4282) for regular Lego plates. The next longest plain-ish plate is probably the 6x28 (#5301, 5309, 4093), but these are thicker than typical plates.
For regular tiles I think the 1x8 (#4162) and 2x4 (#87079) are the longest. Outside of the 2x? they made some odd-ball Scala tiles at 3x6 (#6934) and 8 x ...
No restrictions on the materials.
Well then, probably a component to the old wooden furniture LEGO used to produce, like these:
5003483 - 3-Seat Playtable Creative Play Station Center Pack Duplo
Or the similarly designed 4509g - 3-Seat Playtable, 5004063 - 3-Seat Playtable, or 5003468 - 3-Seat Playtable Creative Play Station Center Pack.
IF-LTW2C - ...
You'll have to ask my vacuum cleaner, It might have escaped me ;).
It depends on what qualifies as "Lego component", though. Made by Lego for Lego would be one of the obvious restrictions, I assume. Is there a restriction on material? If not, it's probably hard to beat the smaller ones of the stickers, but I'd be reluctant to consider them as qualifying, ...
If you could design using Technic Axle 32 as your primary member that would probably be cheapest. You can get 500 of them for under $1 each on BrickLink, and making an Eiffel Tower shape out of those could be fairly strong. You'd be using axles in compression which isn't ideal so you'd need to be careful about bending forces, but in terms of cost per metre ...
I've always thought those flat, round 1x1 pieces were the smallest sphere-esque shape. Most of the other pieces here are longer in at least one dimension than these guys.
This is probably the smallest LEGO brick that is compatible with a stud/tube connection.
There's a version with a hole in the stud that is 'smaller' in that it weighs less, although the ...
Just using bricks the cost argument becomes more important. Unfortunately large quantities of bricks really require that you deal with The Lego Group directly (and they're usually quite happy to deal). For rough price guides we can look at bricklink again. Sorting by quantity available from a single seller for some common parts (we don't care about price per ...
The key point that the team at The Open University calculated made was that while you could in theory build a tower about 3.5km high of bricks before the ones at the bottom would be crushed by the weight of the ones above - this was based on the load-bearing ability of a single 2x2 brick - they also stated that a 2x4 would fail sooner (less support on the ...