About a year ago, we had some construction work done on our house which resulted in about half of our backyard getting torn up (the area closest to the house). After the construction was over, we had the ripped-up area seeded. Now that the grass has grown in, we have a couple of problems:

(a) Most of the new grass is lighter in color than the old grass, although there are a couple of spots in the new grass that look like the old grass (in terms of depth of color). This is especially noticeable before mowing, and is less noticeable after. The effect is that the lawn looks splotchy.

(b) The new grass grows at a different rate than the old grass. At this time of year, I mow about once a week. Using my reel mower, I can see that the mower is definitely clipping the old grass, but I see very little in terms of clippings from the new grass.

(c) The new grass, after growing for about a week, gets random tall shoots or spikes (with seeds), where the old grass seems to grow at a pretty uniform rate with no shoots or spikes. So, after I mow, I end up using a clipper, which is not a lot of fun.

My best guess is that the new grass is a different variety than the old, but is there a way to reseed the new grass without tearing it out and starting all over again? Or, is there another solution you can think of?