Are balsam trees and lime trees the same family?
No, they are not. Balsam's botanical name is Abeis balsamea or Pinus balsamea, depending on who you ask. Lime is Tilia Europoea (though there are many species and varieties of lime, so this may vary.)
The first word in the botanical name will name the family. The second the species. So, as the botanical family names are different, they are not in the same family.
I would like to know the medicinal qualities and properties of arrowhead balsam and its root. It is a wild plant that grows on grassy slopes in Canada and the USA. I have seen it all around the Colville, Wa area and the west Kootenay area of Canada.
I think you mean the arrow-leaf balsamroot (Balsamorhiza sagittata), which is also native to many parts of the U.S. as well as Canada. The sap has been used as an antiseptic for minor wounds, and while the entire plant is edible, this same bitter-tasting sap isn't particularly yummy on the palate. However, the large taproot is said to be far more pleasing. This article has more information on the plant: http://www.mtnativeplants.org/filelib/14.pdf
A forty year old balsam fir is showing signs of decline. Foliage is patchie and some limbs are bare of needles. Is this a recognized condition?
This could be a needle cast disease.
This article will help.
annual balsam flower for flower bed
Yes, deadheading the flowers will encourage continued blooms.
I have used garden powder but doesn't seem to help stop the holes or yellowing.
Depending on the powder that you used, it may not have been a fungicide. This is what will be necessary to kill off a bacterial infection, which is what sounds like it happening. I cannot say with certainty, as your photo did not come through.
Here are some articles that will help you to use fungicides correctly, and to care for the tree:
I guess I should have planted them in the soil by now, but the weather is so hot.
You may want to wait for cooler weather, depending upon how tall the seedlings have grown. Here's an article that may help:
plant Plant is completely drooping... O always feel it needs water... Bt soil is always sticky
Sounds like you need to repot the plant in fresh soil and then make sure to let the soil start to dry between waterings.