Use a good sharp knife or a pruning clipper. A nice clean cut will heal faster and use less of the plants strength than a ragged one from a shovel. Also in some cases the soil may introduce a virus or other pathogen and jaming a stem into the ground with a shovel could cause the open wound to pick something up.
keeping pruning tools clean is important too, to prevent the spread of possible problems
Arthur the Date Palm Guy

Wayne,
I would say you should keep the soil watered quite regularily. Try not letting it get to soggy, or too dry. Sorry I can't tell you how many gallons needed. Some think that fluctuating moisture levels in the soil can cause an A.G. to split. Going from quite dry to very wet, could be a problem. In hot weather, I'd probably give it a good deep watering every 3 days or so, if no rain comes. Maybe more often, if your soil doesn't hold water well. I'd inspect the moisture in the soil, and use your judgement. Different soils, and climates would call for different watering schedules. I would let the soil dry out at least a little on top, before watering again. I've heard that the roots can extend a number of feet farther than the plant's canopy. So I'd water accordingly. Maybe 4-5 ft. around the leaves?
As the plants get older, it seems common for some of the first leaves to die off. Maybe they wear out. I wouldn't worry too much about it. They new leaves you have going, can take over.
If you have a pumpkin you're going to keep, I'd cut off those secondaries that are going to be crowding it. If you're not sure if the pumpkin is a keeper, you can let them be for now, unless the vines or the leaves are in danger of rubbing against the pumpkin already.
These are just my educated thoughts and opinions.

Douglas

Thanks SoftMentor and Douglas. One thing that's interesting is I don't know how far the roots will ultimately extend for the plant. I have a hard clay soil here and I'm essentially doing "container gardening" where I've dug a 3x3x3 foot hole for the AG's soil. Mind you, we did have a ton of rain right up until june so the soil is less hard than it used to be. Maybe I will get substantial root growth after all. We'll see. thanks again.

Wayne,
Are you letting the vines run out into the grass?
If so, I think someone down south grew similarily last year, and ended up with one over 500 lbs.
This method would be much less work, with only a 3' X 3' area to weed, water, and fertilize the soil.

Douglas

Hi Douglas, yes, the vines are running into the grass. We get no rain here in the summer, so the grass is drying up right now. I haven't even thought of fertilizing. Do you have any low-cost ideas for this ? thanks.

Wayne,
I've been using Neptune's Harvest fish and seaweed fertilizer. I bought a 36 oz. bottle for around $10.
I use it to fetilize the young plants with a soil drench around the planting area. I've been using 2.5 gallons of water, mixed with 2.5 oz. of Neptunes, and about 2 oz. feed grade molasses(1 gal. for $7). My plants are at the 4-5 ft. range, and soon I'll likely just foliar feed, and rely on the soil fertility.
I've been foliar feeding, and will continue once or twice a week through most of the season. I use a gallon hand pump sprayer, and add 1 oz. Neptune's and 1 oz. molasses per gallon of water. I spray this on all the leaves of my A.G. plants.
I'm no fertilization expert. You could also check out what Don Langevin recommends in his books.
If I were you, I'd probably fertilize the 3' X 3' soil area once or twice a week with Neptune's and molasses. I think the bottle recommends once a week for plants, but for an A.G., coupled with your small open soil area, twice a week may be better. Your call. For 3' X 3', you may need 5 gallons or more of fertilization solution.
I'd foliar feed the plant, as I do, once or twice a week. I foliar feed in the evening, when temps. cool down.

You could also water the lawn where your A.G. is growing. One fellow growing out over the grass, stated that the roots that form at each leaf node, actually borrowed into the ground, even though it was sod.
I should add that if you do use the Neptune's, it may be more economical to buy the gallon jug of it, if you will use that much. I bought mine at a local chain store called Fleet Farm. The local store only had the liter bottle, so I have to buy another soon. Maybe local garden centers carry it there.
I hope this helps.

Douglas

Hi Douglas, thanks. Actually, my plant is not growing on a lawn but in the field behind our house. The soil is very hard clay and it's really field grass and weeds out there. I doubt if the rootlets will find a place to burrow in. I'll do my best this weekend to locate some of the Neptune's. thanks