Loan servicing means collecting the payment, applying it to principal, interest and escrow, and keeping the record of it. On a subject-to deal the bank's servicer keeps doing that job on the underlying loan. What the third party companies do is sit between you and that servicer: they take your money on a schedule, send the payment to the lender, hold and disburse any seller-carry note payments, and produce a statement both you and the seller can look at.
That third piece is the reason to use one. The seller's name is on that loan for years, and a neutral party generating a monthly record of every payment made is what keeps a nervous seller from calling the bank. Typical pricing I'd expect you to be quoted is a setup fee somewhere around 100 to 300 dollars per loan and a monthly fee in the 20 to 60 dollar range, with extra if they're also administering a seller note or an escrow. Confirm the current fee schedule in writing, since these companies price differently and some won't take a file where the borrower of record isn't their client.
On the password: you're right to want out of that arrangement. The cleaner mechanism is a third-party authorization or limited power of attorney signed by the seller at closing and filed with the servicer, which lets you call in, get payoff and escrow figures, and receive copies of notices. Whether a given servicer honors it, and what form they demand, varies by servicer, so ask them for their form before closing rather than after.
Also get the mailing address on the loan changed to one you control, or you'll never see the escrow analysis.