Take those in order.
Do not call and consent rules for calls and texts generally look at who the call was made on behalf of, so using a vendor doesn't automatically put the exposure on the vendor alone. How that applies to any specific arrangement depends on the statute and the facts, and a lawyer who handles telemarketing compliance is the person to confirm your own position in writing.
"It's B2B so it's exempt" is not a general exemption you can rely on. Some rules do treat business-to-business contact differently, and a homeowner reached at their personal cell about their own house is not the situation those carve-outs describe. Treat that advice as wrong until an attorney tells you otherwise. On top of the federal layer, a number of states have their own calling and texting statutes with tighter consent and time-of-day rules, and they vary by state, so where your list sits changes the answer.
Litigator lists are real. Vendors maintain databases of phone numbers tied to people with a history of filing claims against callers, and scrubbing against them is sold per number, often in fractions of a cent to a few cents. It reduces one specific risk and doesn't make anything compliant on its own.
The practical thing to ask for before you sign: an indemnity clause naming you, proof the vendor scrubs and keeps records of it, and their opt-out handling procedure. Ask what insurance they carry for this specifically. General errors and omissions policies commonly exclude claims arising from calling and texting statutes, so an insurance certificate isn't the comfort it looks like unless the exclusion list says otherwise.