A DTI calculation isn't hard, just need to know your income and your debts. In your case existing debts are all the minimum payments which you can get off Credit Karma and your IRS payment plan monthly amount, and then add that to the PITI which you can get off any mortgage calculator on the net, and divide that through by gross monthly income and that's the almighty backend (housing included) ratio which is what the lenders are really looking at. If that's below the threshold, don't pay off the car, if it's not... then it's worth having that conversation as there might be cheaper ways to reduce that number.
Regarding the IRS you'd need to have the new payment plan in hand, AFAIK current rules are you only need to have made one payment before closing (according to the first hit on Google, which is more friendly than what I recall but I would do a more detailed check if it were me).
I will say though that while there are financially stategic reasons to owe the IRS money, having a semi-recent 28K shortfall and then trying to tack a mortgage on top of it, I'd look really hard at my finances.
Gotcha. I will try to find out mortgage scores, but our actual FICO scores turn out to be Ex683 TU690 and EQ671
As for the IRS debt, our monthly payment currently is 390. I expect we will be paying around 800 a month but our new plan is not set in place yet, we have only just filed all 3 years on Friday. Also in regards to the IRS, I know what it looks like - bad, lol. Our situation was we leased a semi from a "friend" and thus became owner-operators. The truck broke down constantly due to regen issues. The worst break down cost us 30k in repairs, as well as 3 weeks of not working/no income while it was down. This destroyed our credit, we were constantly trying to stay caught up - nevermind saving - and then whenever we did get a tiny bit ahead there was other maintenance - new tires, insurance, plates, etc. But the REAL kicker here is the 1099's from the "friend". Saying we made 260k in 2017. Our write offs took us down to 160k. Our deposits?? 70k. Did not even get paystubs. It's very frustrating and I am glad we are out of that situation, as I fully believe quite a lot of money was taken from us that we still paid tax on. In Jan 2019 our Eq score was 544, so our lives (and scores!) have improved vastly since walking away from that owner-operator mess. AND we have health insurance! AND taxes pulled.
So, we were in a very bad place but no longer are, and our tax situation should NEVER be like this again. We were stupid to allow it to happen, I can't deny that. Whether this makes a difference in our chances, I do not know. But I hope not. Home ownership is literally all we want out of life 
We've been trying hard to turn around and have been waiting a long time to be in the right place.
Total income: made 113k in 2019 and expect to continue making the same
DTI: Credit Karma says 1767 monthly debt. Add in the current 390 IRS bill for 2157. Monthly income is around 8k, so that puts us at 27%. Of course, there is still the credit card I mentioned that will be paid off in April, and paying the car off 600/mo would make a huge difference here. However, most responses so far have recommended not paying off the car so I probably won't do that now. Would be nice if a LO indeed left it out with its payoff date approaching next year.
Most of our monthly debt is in car payments at this point. In addition to the 600/mo, we also have a 450, 300, and 177.
If our IRS payment plan does go up to 800 that looks to be around 32% DTI. No student loans, child support, alimony, etc.
- All minimum payments listed on credit cards and other revolvers on credit report.
- The auto loan
- any other installment monthly payments.
- The IRS debt payment
- Any other debts not on the credit report but fortunately this is pretty rare these days other than business cards.
Then add the PITI (payment interest taxes insurance) that you got from that calculator. If that is coming up less than 43% you're good.
There are some loan products which can go higher but I would shoot for 43% personally. Also one note you will likely need more than 5K down on 200k (or did you mean 5%?), and there are closing costs to consider too.
I am buying a 325k place at 5% down with no stupid lender fees or points and I'm at like 23.5k total. That can get cheaper, for example buying existing property is probably cheaper than new construction, but it's good to have cash as mortgages are expensive to get, long term absolutely the right call financially though.
I guess what I am trying to say is if you can get under 43% saving money is the right path; even 50% maybe but that restricts your loan options and long term it's less of a cushion if life goes sideways financially.
