Lots to unpack here. My initial thoughts are to underwrite the deal, determine what you need to buy the property for, and stick to your guns. It doesn't matter what the list price is, what the agent is saying, or whether there are other offers. That is all just noise. If you're putting up several hundred thousand and getting a multi-six-figure mortgage, you need to be confident in your financial decisions. It's always caveat emptor out there (buyer beware). Remember that most properties are not good investments. Every house has a number that makes sense (even if that number is negative; aka they pay you to take it).
Don't fall in love with the deal and make emotional financial decisions. This is called naming the puppy and once you've done that your chances of making sound financial decisions is greatly decreased. Trust me, it isn't worth it! It is better to miss out on a potentially great deal than lose a ton of money on a bad investment. There are always more deals. If you're feeling the pressure to do this deal, even if the numbers don't work for you, then deal flow is your main problem to solve. If you had 5 other great houses you were evaluating on attractive terms, would you be stressing about this, or telling the agent to pound sand and standing firm.
As far as the seller financing goes, this needs to be written in the Purchase and Sale agreement, not "get seller financing later".
Now on to your questions:
1. We can't know for certain, but high pressure is not a good sign for your best interest.
2. Loan contingency is for you to get a loan. Seller financing is a purchasing term. You're talking about 2 separate items on the contract. The deal may involve a loan, a loan contingency, seller financing, or any/all/none of these items.
3. Dual agency is a legal and legitamite practice, but involves potential conflicts of interest. Therefore disclosure is paramount and the fact that it is lacking here is extremely concerning. Given your lack of experience, I would get a different agent to write up the offer for you, not use the listing agent.
4. They were bluffing on the other offers or their price/terms. Why indeed?
5. Seller financing is a tax mitigation strategy. Yes, they can foreclose, but that is not ideal for them. It may improve their cash-flows rather than getting a large chunk of cash upfront, they can get interest on the money and a consistent paycheck without any work. True mailbox money.
Not everything moral is legal and not everything legal is moral. You already know what to do here, you just want confirmation that you're correct. Trust your gut.