I am sorry but allot of the posts are correct in regards to the welds you are showing.
There is no penetration I can see in the welds pictured; they are sitting on top of the tube stock.
You can continue and in the not distant future these welds will crack loose and become a serious problem.
The most important aspect of welding is laying of the "root" weld. This is at most times the very first weld made; it has to penetrate all the way through the pieces being welded. The "cap" welds made after the root weld are also important; but don't have to look pretty to have strength.
Depending on the tube thickness a bevel is a very good idea to put on the tube end your butt welding to another to give better chance of penetration.
From what I can see you are having a problem of the "weld" running down the piece?
You need to readjust your heat and adjust the wire feed if your using a mig?
Is it flux core or gas?
In parting you have done a fantastic job BUT I would strongly suggest getting those welds redone. It will be far cheaper and allot easier now than later.
Here is a link for some examples.