Remove the screws that hold the countertop to the cabinets, and lift it off.
Not if they were glued. But that's not the normal method of fastening them. Normally, countertops are held in place by screws inserted up through corner braces at the tops of the base cabinets, into the bottom of the countertop.
Usually, the backsplash is part of the countertop, and comes off when the countertop does.
Look underneath for screws, you never know often they are not fastened well or at all , Does it lift, no screws, then its glued, how well who knows. Counters are heavy fastening them isnt always necessary for long heavy pieces.
Well of course this depends on whether they are factory cabinets and counter tops or ones someone built some years ago. More info would help. What is your plan afterwards? If you are putting on new Formica and the counter to back splash joint is square, just sand the old Formica and cement new on top of it. Look for screws underneath as others have said if these are "factory" counter tops. Back splash and counter top will be one pc. If "built in place" no telling how back splash is attached, to counter top or to wall.
You can saw the entire counter top off, Formica and underlayment, with a reciprocating saw and you don't have to be extremely careful since you new top will likely have a lip extending down over the outside edge of face frames and will cover up jagged saw cut edge, just don't over do it. It was customary when fabricating cabinets in place years ago to nail the underlayment thru the top into the framing then cement Formica or similar material over the top. If this is the case, it will probably be nailed thru into the dividers also.
It depends on whether the counter is nailed down, or glued. Mine was only glued, so a few good whacks on a pry bar (that's what you need, not a screwdriver) brought the whole thing up.
I had a little 13" section by the stove, that I messed around with first.
Most likely - mine did. Go slow, see how it goes, use the pry bar in the glued joint if you need. As long as there's enough left & even enough to support whatever you're putting down next, you're fine.
Score along the top of the backsplash with a razor, so you don't bring the wall with you. It's likely that the backsplash will come out with the counter, though it may crack at the corner first.
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