One of the best ways to help strengthen the seedlings is with more intense light and air movement. You can turn a fan on low and have it blow above the seedlings, not directly on them. You can let the fan run for at least 8 hours a day or more.
With most plants you can't plant them deeper then they were growing in the pot. You already know you can do that with tomatoes. In my search for info about this I have discovered you can plant broccoli deeper.
This site, with great info about growing pumpkins, says (second link is the page for this info):
Pumpkins, squash & cucumbers are all in the same cucurbit family but that doesn't mean that each particular veggie can be treated the same.
4. Dig a hole in the bed you prepared deep enough for the entire pot.
5. Fill in soil around the pot and plant. You can cover any or all of the stem up to the primary(first) set of leaves.
For your cucumbers I found this as the last sentence under 'Maintenance and care' which leads me to believe you can plant them deeper.
I have not been able to find any info for planting either pole or bush beans or squash any deeper.
Mounding soil around the base of the plants can discourage squash borers from laying eggs.
You might find these growing guides helpful.
You can use the above site to get the Latin names of your plants or search by common name at this site for more info.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.