1.) Although your 5th pic 'suggests' the limbs are straight, be SURE they are before stringing it. Minor twist can be bumped straight, major twist is another matter.
2.) If it passes #1, replace the string with (as mentioned before) B-50 dacron. They are fairly cheap, and the cost is worth it considering the 'other cost' you might pay (a string that breaks at full draw is not fun).
3.) After putting on the new string, use a bow stringer and (as said before) be careful...do it a small amount at a time to flex the limbs gently. Look for signs of major twist as you put more pressure on the stringer...sometimes twist doesn't show up on old bows until pressure is applied. If they twist significantly during stringing, STOP. The bow has issues needing fixing before going further, or it's a wall hanger.
4.) If the bow strings up normally, again be careful when drawing it. Look and listen for odd flex noises or possible delam along the limb edges/limb tips. Go slowly until reaching full draw, then careful 'bounce' the draw as final stress test. If all is/sounds/looks ok, shoot an test arrow. If bow sounds, feels, and shoots ok then you probably have a keeper.
5.) Unstring it and clean up with Goo-Gone, not water or mineral spirits. GG won't harm the finish and it's an excellent cleaner for wood surfaces.
Hope it turns out well and you can enjoy it. BY the way, DM Howatts are great bows but tend to have some twist issues over time even when handled and stored properly (at least the three I've owned did). If it passes the above tests and seems ok, just be sure to check the limbs carefully eery once in awhile for twist. With straight/solid limbs that bow should be a great shooter.