A lot of this info is in the Sovereign/Excalibur Batteries Sticky, but here's a quick run down...From memory the Sovereign and so I would assume the Excal because it's just a waterproof Sovereign, draws around 50 to 69ma or so. So do the math. What is the capacity of the stock rechargeable pack you have? Assuming it's 1000ma like the Sovereign (isn't it 800ma on the Excal?) divide the amp draw into the capacity. 1000ma / 50ma = about 20 hours of run time. But if you've charged the pack and it's sat for a while, like say a week or more, the capacity will drain over time, so don't expect to get that full 20 hours out of it. Some nimhs/nicads are worse than others at self draining on the shelf, so run time will vairy.
For me, if I'm hunting say 3 five hour days on a 1000ma pack in a week, that's about all I'll push my luck and time for a re-charge, but especially when new it's good to run a nimh or nicad pack down as far as possible for say the first 5 chargings. That will excercise the pack and get more run time out of it. I also like to do this say about 2 or 3 times a year. Many people strongly believe a nimh or nicad should never be drained all the way dead, but I fall into the camp of draining them dead on a car tail light bulb 2 or 3 times a year, and re-charging about 3 or 4 times in a row, to fully excercise the pack and keep it in top shape.
Many won't do this, because there is a risk of the pack reversing polarity. Never had that happen myself, because IMO the odds of that happening are exist to a large extent if I let the pack sit dead for say days after it's been drained. So long as I charge it right away I've never had that problem, and I feel it's the only way to get the most capacity out of the pack myself, but again some others don't agree with doing that kind of full drain. That debate has been going on on the web among the RC plane/car crowd for years, so take your pick as to what you believe is the best way to do it. I make no claims to being right about how I feel about it. It's just what I do with my packs, and I'm sure others have had problems so they have good reason to feel the way they do about not draining a pack that far down.
Even if I drain it until the light bulb goes dead, I'll let the pack sit hooked up to the bulb for about another 30 minutes or so, and once the load (light bulb) is removed, the pack starts springing back up in voltage right away anyway, so I don't fear the reverse polarity thing myself, especially since I then right away throw it back on the charger. But many say you are risking reverse polarity of a cell doing that, so you might want to heed that advice and not follow my routine. Just running the pack to the low battery alarm on a hunt 4 or 5 times in a row should be enough to excercise it and get the capacity increased, both when new and also as a way to condition the pack a few times a year (done say 3 to 5 times in a row on sequential hunts).
The alkaline pack with fresh batteries run time? Look in the manual and see what it says. If you don't have a manual in the Excalibur Accesseries sticky (or at least in the Sovereign one) there is a link to Minelab's web page with all the manuals for the Sovereigns and Excals listed. I run a 3 cell lipo in my GT for weight savings and other perks, so I don't know off hand what kind of run time to expect. I'm sure others with Excals will chime in and tell you what kind of run time they get with certain brand name batteries. You might also look into the Energizer Lithium batteries. They are more expensive than regular AAs, but in addition to being lighter they also will give I think Energizer claims 3 to 4 times the run time, so the longer run time more than makes up for the slightly extra cost.
How long to charge? Look on your wall transformer for it's MA output. Let's say it's 100ma. Divide that into the capacity of the pack and that's roughly how long to charge a dead pack. Overshoot it by an hour or so, because the charging process is not very efficient so it often takes longer than the math says, and also good cells often hold more capacity than the label says, by say maybe 300ma or so on a 1000ma pack.
You can also figure out roughly how much capacity was taken out of a fully charged pack on a hunt. Figure maybe 60ma average for current drain while hunting, so multiply that by the # of hours hunted, and then divide that # by the output of your wall transformer, and now you have an idea of how long it should take to charge the pack back up to full capacity again. Again, I'd overshoot that # by say an hour or so just to make up for the inefficient charging process. Also consider how long the pack has sat on the shelf. If it's been weeks maybe another 400ma or so is probably drained. Add that into the math.
Far as I know (?) the Excalibur pack/wall transformer doesn't indicate when the pack is fully charged, so you might want to look into an aftermarket charger that will clearly show when the pack is done. Some guys in threads in the Battery sticky links to have some info on that for what they like to use for their Excal packs. Just make sure the amp rate isn't say 1C (equal to the capacity of the pack, or for example 1 amp for a 1000ma pack, or .8 amps for an 800ma pack) or higher, because that tends to shorten the life of the pack. Especially if the pack is inside the POD and is getting hot from too high of a charge rate. Feel the pack while charging. Hot? It's being charged too fast. Luke warm is OK, but in general heat destroys a pack over time.
I'd shoot for say 1/2C (1/2 capacity) or less at the most for most charging. In a hurry if the charger lets you set the amp rate 1C should be OK here and there provided the pack isn't getting hot. I think I remember Kered saying anyway that the Excal stock pack has a thermistor in it, so if you try to charge too fast and it gets hot, the thermistor will pop and the charging will be interupted. Once it cools back down it'll re-make the connection, but that's a safety feature and should never be used to govern charging. Thermistors have a limited life, so one day it'll pop and never re-make that connection.
Some guys are using an aftermarket 1600ma nimh pack in the POD, which I think should just about double your run time over the stock pack, but if you use the stock charger and say it's 100ma, that means 16 hours to charge it. The wall transformer is putting out a trickle charge, which is pointless for being easy on the battery. And another thing, unlike nicads, nimhs don't like being trickle charged once they are fully peaked, so over time that could shorten the pack life if you let it sit on the wall transformer for many hours after the pack is fully charged.
I'm only going from what little I've read on the Excal batteries since I never owned one. If you look in the Battery sticky you'll find links to a few of Kered's threads where he goes into specifics more, and also to other threads where other Excalibur guys give their advice on both the stock wall transformer (charger), and using aftermarket ones. Being that I've never played with an Excal stock rechargeable pack, don't take my advice and confirm it on your own by reading what they have to say in those threads, and I'm also sure some others will probably chime in here and set you straight on anything I may have had a bit wrong.