As stated above, clarify what the 50% is based on. A 50% UPB trade in Texas would be a pretty nice margin. Be aware that the offer here may not be approved by the bank's committee yet. So, it is important to understand how firm or what approval process the offer will go through. A committee may not see the loan sale the same way this bank employee does and thus seek more money.
It sounds like the bank has, to some degree, codified a selling price (50%). So next steps would be ask for access to the file. You will want to get a title report to verify the lien priority and understand any other encumbrances on title. That will lead you into most of your disposition here based on the story.
Paying for a loan comes after you conduct due diligence. I wouldn't escrow any funds or put up any deposit to conduct due diligence. Those are uncommon concepts in loan sales.
The amount of time afforded to conduct due diligence is negotiated between you and the Seller. You want sufficient time and access to the file to look into what you need to look into. Then you will want sufficient time to review and agree to the terms of sale. For a single loan you should be able to wrap it up within 3 to 4 weeks.
Do not fall victim of negotiating two different assets here. The value of the collateral is what it is. You have your value. The Seller will have theirs. The only thing you want to talk about is what you are willing to pay for the asset that is for sale which is the loan not the real property. When transactions start discussing both loan sale price and RE Value they get jumbled up and can fall apart. Assume you won't agree on the same value of the house and just structure your purchase for the loan to suit your needs. The Seller either takes the deal or doesn't. You won't be able to persuade them to see from your vantage point.
I disagree with the idea above of moving toward a short sale solution. This could backfire on you. Depending on how the purchase price offer lines up if you take the deed from the Owner and then move to short the bank, the transaction could go in front of committee and be rejected. That leaves you having to come up with more money than may have been originally planned.
I would buy the loan and then deal with the Owner. You can still do a DIL even if there are junior liens. Doing a DIL in alternate company won't merge your interests as a Mortgagee. This will retain a power of foreclosure for you wil gaining control of both the property and the loan. In this case, look to control as much of this as possible as that will make disposition easier for you.
Your attorney can review the purchase contract and perhaps order and review title. Not too sure they will dig too far into the file outside of that. From the post, the deal seems pretty straight forward. Just remember, until it is done, things can change. Don't fall victim to any party changing what you thought was going to be an agreed item.