I bought it for $235,000 two years ago and have made some value-add improvements (like raising rents, adding washer/dryer,etc). 

Purchase price: $800,000 Cash invested: $200,000 Sale price: $4,875,000 Bought from FDIC, did many improvements, increased rent refied 2X What made you interested in investing in this type of deal?

I think you are right, non conforming can be a can of worms especially if the conversion was unpermitted or you ever want to improve the property in the future

Have you improved any of the units?

Also adding value with improvements over time.

Now after not doing a single improvement on the home the ex wants half of the sale amount.There was no agreement in place when the house was purchased as to what would happen when it would be sold.Legally how would this be approached.

So, as long as you do things that make sense and stick to it investments will improve with time.

What would the IRS consider improvements that must be depreciated? 

In terms of improving targeting, I have heard that you can purchase something akin to a title search here in Ontario through MPAC (or maybe your local municipality) that at least gives you the names of current owners but each search costs about $8 so you don't want to do many of those!

A CPA would know whether or not you could take bonus depreciation on the capitalized improvements, but since you already know what the cost was, there is no need for a cost segregation.