I am in the piedmont also, what a lot of people refer to as zone 7 but I don't believe in zones so I don't use them myself but the temps you mention are similar to here. I would never get to raise the height much because come september when the temperature plummets so does the growth rate of this grass and even with fertilizer I haven't been able to get a significant increase in height after cutting it short for the whole season. Nothing major bad has happened to it. Lost a little bit last year but it wasn't a big deal bad might have actually been from a late freeze. In this area, this is when the optimal growing time for Bermuda comes to an end. It will slow down and lighten up and the zig zag marks come next month then it's all over. So I hope you enjoyed it while it lasted.

Central Indiana would be the cool grass types. KY Blue, Tall Fescue and Rye and the other small grasses that come in the mixtures. Go to a farm store and they will have grass mixtures and pure varieties for your area. Since I happend to like the thick lush of KY Blue, I normally just start over seeding with it and over time the yard will be predominently KY Blue. Now would be a good time to over seed. Buy one of their pull behind broadcast seeders. They are a good thing to have around. Get one that will hold about 100 lbs. Now would also be a good time to put down crabgrass killer mixed into your fertilizer. You can most likely get it at you local agricultural farm chemical supplier. The other useful tool to have is a small 14-25 gallon pull behind weed sprayer. Spring is not the best time to spray for weeds, but it is second best. I use Amine D with the ingrediant that will get rid of clover. Ask the guys at the Fertilizer Dealer (Agri Chem Supplies). May also be a feed and fertilizer store.

It depends on your climate but this early in your season they should come back given sufficient water.

Cut so that you don't mow all the green out. I would not bag the clippings, they are a natural source of nitrogen. You might suck up some of your seeds and/or growing medium (mulch/peat moss/etc) as well. Use the 1/3 rule. So for example: if you have 3" grass you can cut 1" off. So you don't mow very often to keep the lawn maintained. If you want really thick Bermuda you want to cut it as close to 1" as possible WITHOUT scalping or mowing out the green. Downside, or upside in my case, is that you have to mow really often because you can only cut 1/3" off of 1" grass. So you can plan on mowing about every 3-4 days. Bermuda loves a close cut IF you can get your ground level. Where most people screw up is mowing too low and putting circles in their otherwise beautiful Bermuda lawns. Mowing out all the green mows out all the energy the grass has stored. I use a Tru-cut 27" and mow at about 1.25". It feels like I'm running a snow blower if I don't cut at least every 4th day. So many little green clippings spewing forward. Sweet satisfaction though! If you can afford it, get you a reel mower. And a gas one (Tru-Cut, Mclane, etc) with a roller bar on the front. They regularly go on craigslist or from a dealer (used) for about $500-$600. You can sharpen yourself with a little youtube research. You'll be able to keep it really really low and make your lawn look like a fairway, stripes and all. All your neighbors will be envious too!