As an example, I've heard of cases where the seller has accepted an offer with a 5% reduction on the purchase price, in order for the 2.5% earnest money deposit to go hard (nonrefundable) on day 1 of the contract.

Have they done price reductions during that time?

Also, has anyone ever tried actually offering a full or close to full price on a rehab with X day inspection period and hiring a GC to get a legitimate quote then renegotiating price reductions due to repairs?

I would negotiate a significant reduction in the purchase price or have the seller get rid of the tenant allowing you to find your own tenant at closing.The owner could of course simply pay you the pro rated 10 months rent but that is little consolation and you probably have leverage to get more.

Tenant asked for rate reduction.

Not sure why drastic rent rate reduction is rarely mentioned here but it certainly happened.  

This is the quick and first glance way I look at it.Verify gross rents didn't have first months rent half off or free otherwise stated annual rents per unit actual rent is lower and that rents have not shifted downward since all the lease ups.If lease rates have moved down some of the tenants will want a reduction or leave to go elsewhere.

The 11 unit apartment building has had a price reduction.    

For expense reduction, the first place I'd look is buying a much less expensive car.

After repairing the septic violation (estimated $20K), I would go through the reduction hearing process to have the lien reduced as much as possible.