For example Our home values have more than doubled in the last 10 years but the rents are only up about 80%, so the returns on equity are decreasing. 

Here in chicago LTR rents are way up since 2021 many 20-25% higher so those still work and I have not seen any decrease in demand on investment purchases. 

Assuming I purchase a house with the intent to fix and flip in a 6 month window, do the carrying costs I pay increase my cost basis, such that my taxable profit is decreased?

You can find higher ROI (on paper) here and probably in other cities…but the probability of actually collecting rent significantly decreases.

Now that the lease is expiring soon ,the tenants are asking for a rent decrease because five people will move out.

Since as inventory of rental options decrease, the demand for those that effectively operate as AirBnB's should theoretically increase. 

I suspect as rates continue to decrease terms will begin to improve and more buyers will re-enter the market/ be able to pull trapped equity out of their recently completed projects.

The median sale price rose to $350,000, reflecting a substantial 10.8% increase from the previous year.Total housing inventory showed a notable 19.2% increase from a year ago which is much needed.Half of the homes sold were under contract in 23 days or less, a slight increase from the previous month but a decrease from a year ago.For sellers, 43.5% of homes sold for the asking price or above, with 21.5% selling for more than the asking price.

. - December saw the largest drop in leads, the number of leads decreased 18% throughout our markets. - January experienced a significant increase in demand.

As rates continue to decrease, more investors will come off the sidelines.