This involves rolling your shares from your 401k into a brokerage account (Taxable event and potentially a 10% penalty if you're under 59.5 y/o). 

In that case, the taxable income is reduced, but usually not by a significant enough amount to realize a substantial "gain" from the rental loss.

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?

Mistakes leading to funds being handled improperly could lead to the IRS blowing up the entire IRA account as a full taxable disbursement. ...liability.

That is taxable in the year you sell the property. 

We do have other investments in the market with our non-taxable assets (401K) which we plan to use post retirement age (60).

I don't think taking cash out in refinance raises your cost basis to calculate your taxable gains at sale unless you used the cash-out refi for an addition to the house. 

Run this by your CPA so they can include your full taxable situation.  

That is your taxable basis.

(income taxes)Additionally, the question of whether to hold until death or gift may also depend on the size of your mother's taxable estate and where you believe the estate tax laws to be headed.