Let us clear up a few basic concepts.
Physics is about studying the way nature is . To start with, this could be descriptive, as it was for centuries before Newton. Descriptive does not answer "why" but "how" questions, in the same way that a map does not really answer "why" the landscape is like that, but describes as accurately as possible the "how" the landscape really is.
After the brilliant work of Newton it was possible for physics to grow in leaps and bounds because the descriptive method was replaced by a mathematical modelling method. Mathematical equations, with axioms, theorems and lemas were found to describe all the available data and as a great bonus, predict future or unseen behaviors.
Since then the holy grail of Physics is to find a mathematical theory which will describe all the available data with a coherent mathematical framework which will also be used to predict unseen as yet phenomena.
These theories can tell us How . They can never tell us Why? unless we give a religious significance to the mathematical framework. In that sense the why is answered, in your case, because that is the way the group structure that describes the data is in the theory accepted up to now. i.e. the weak forces are short range because they have a massive exchange, and the strong forces because the exchange particle, the gluon, has self interaction which becomes equivalent to a massive exchange in some sense.
If we accept that the current theory/model is inevitable ( what I mean by religious significance) then this is the answer of why.
In my opinion the real answer is that : this is what the data tells us , whether we like it or not, and our mathematical tools encode it and show us how from a few assumptions the complexity of the interactions can be modeled and predictions made of new data to be observed.
Why are the strong and weak nuclear forces short range?
Because that is what observations tell us, with innumerable experiments.
Are quarks confined or welded together?
Quarks are an intelligent model result and their existence is consistent with the standard model , and no, they are not welded because experiments show us they can permute into other configurations than the original ones: the three on three quarks at LHC generate a number of different quarks etc.
Why are elementary particles confined at short range?
Some in the table of the link above are confined, the quarks. the rest in the table are not confined:
The quarks are confined because the colored gluons exchanged display a collective force that increases with the separation between the quarks and it gives rise to confinement.
The Standard Model of elementary particles, with the three generations of matter, gauge bosons in the fourth column and the Higgs boson in the fifth.
Or is color confinement color welding?
No, in no sense of welding can quarks be considered welded. Glued with elastic glue, yes.