If they are will it be contingent on selling you their property to find a suitable replacement? 

I went and looked at the property again the following day and made an offer at 80K with an inspection contingency.

The tax docs list as a 2-unit but the owners + seller's agent insist they have zoning compliance paperwork that it's a 3-unit - our offer has a contingency on getting the zoning paperwork for a 3 unit.My question is related to the garden unit - what constitutes a legal bedroom?

@Rick Thompson in general the reason to use Heloc and pay cash is to get a better deal by removing financing contingency and being able to close quickly.

I had an inspection contingency in there so that if anything was missing/damaged/undisclosed I had the ability to make it right, and if not I was in the clear.

There is going to be a special assessment soon of about 2,000 + 2 years of an additional 150/month.I can't deal with tenants calling me constantly with every little thing that is wrong (my pipes tend to clog) so rental would be contingent on tenant handling these things on their own.If I do sell, I would put the money in a mutual fund.What do you think?

The first appraiser actually did the appraisal as a multi-unit (duplex) but put it contingent on permits and papers from the city/title company.

The anonymity is not an asset protection technic per se, but is a smoke screen that will avoid ambulance chaser or opportunistic lawsuit based on contingency.

Most lenders don't consider an after repair value, and most appraisals don't list an after repair value, which makes me think you're not applying for a conventional loan.Did you already remove the appraisal and / or financing contingency before you got the appraisal back?

The final payment should be contingent upon final inspection (code compliance) and a final walk-thru.