I was going to tack this on the end but I think I should start with it since it may supersede all the below.
Re. the warped boards, because of the great strength and stability of the completed glued-up panel it can be perfectly fine to have a few cupped or twisted boards in the mix.
Source: Woodsmith Magazine
As long as you follow a few basic rules of construction (e.g. try not to mix quarter-sawn and plain-sawn wood, don't mix woods of different MCs, apply enough adhesive and bring the pieces together in sufficient time to fully wet all glue surfaces and last but not least clamp hard to squeeze out all excess glue) you shouldn't have any problems.
In reality I bet that rarely has anyone done a large assembly like this where every board has been absolutely flat and straight! Some of that is budgetary constraints, especially when working in hardwoods, but in large part it is because it just doesn't matter.
I see on some lamination finger joints are used. I am just working with pine and don't have the means to do efficient fingers joints.
I'm theorising here but on some commercial stuff the finger-jointed ends are done merely because that's the way they always do it. There are times where finger-jointed ends may be more for convenience in handling the stock rather than as a means to improved strength, because the strength they do add is not usually required.
In something like an Ikea-type countertop where the panel is predominantly made from pretty short lengths of wood then finger-jointed ends could indeed add some needed strength. But where the top is largely made up of long (especially full-length) boards glued face to face then a few butt joints spaced around the glue-up won't affect strength in any way you'd notice.
the face of the wood should bear most of the burden.
This is correct, the joined faces will hold the piece together. Long-grain glue joints as you know are at least as strong as the wood if done well, so even without being glued together the end butt joints are no more disruptive than if you'd sawed through a piece of solid wood.
Do I actually need to "glue" the butt joints together before laminating them to another piece?
No, you might choose to but it's not necessary. It's fine to just glue them while doing the overall glue-up, as long as you're not losing time and working efficiently (you don't want to have glue partially set on the first few boards before bringing the whole assembly together and adding clamp pressure).
If you want to err on the side of caution size the end grain with diluted glue a few minutes before doing the glue-up, this will maximise the joint strength by preventing the full-strength glue from being over-absorbed.
Do I work like I would a normal whole piece and just laminate the whole thing with clamps on either end?
Depending on the total length, the width (hence the number of glue lines), as well as the type of glue and the temperature and humidity where you're working you may prefer to glue up in sections, thirds or halves of the total top. Once these are fully cured you can then do a very easy final glue-up of the two or three sections to make up the full top.