The standard US flash pasteurization protocol is 161F for 15 seconds. But I usually like to boil my dme until the hot break has happened. Though I'm not sure if that makes a difference.
Adding DME at this point is completely acceptable. Go ahead and aerate the addition with a whisk or something, though, at this point, that's probably not necessary.
To figure out how much you have you need to figure out how many points per gallon it gives you. Usually DME is around 44 (or in other words, 1 pound of DME in 1 gallon of water would result in a 1.044 SG). As stated, if your original wort was 4.5 gallons, and you had an OG of 1.044, you have 198 total gravity points. So if you add in 1.5 pounds of DME boiled in .5 gallon of water, then you have 264 total gravity points divided by 5, or an OG of 1.053. If you boil the DME in less water, the OG will go up, if you use more water, the OG will go down. Basically you can divide 264 by how many gallons of liquid you end up with.
The equation is:
potential ppg x weight of fermentable / volume = SG
BUT!!!
I would be very concerned about your SG readings. According to Beersmith's calculations, with a standard boil-off rate (19%) and cooling shrinkage (4%), in order to end up with 4.5 gallons of 1.044 wort, you would have started with 5 gallons of 1.040 wort. The problem is that means that you only boiled for 20 mins though.
In order to end up with 4.5 gallons with those normal rates mentioned above, you would have started with 5.8 gallons of 1.040 wort. But if you had that much, you would have ended up at 1.051 OG after a 60 minute boil.
So something is off. Either you're not getting to a full boil, or your volume measurements are off, or you measuring the gravity incorrectly.