Universal Turing Machine algorithm


First, I learned this based on these facts:

  1. Turing machine (TM) will be define with 7-tuple Notation, M=<Q,G,b,S,d,q0,F>.
  2. Any computation rules that can use to simulate any possible TM is called Turing-Complete.
  3. Universal TM (UTM) is TM that is Turing-Complete.

Then, the question begins:

  • If we have 7-tuple Notation of any U that is UTM, Is there an algorithm to find initial tape content P that U to simulate any TM T with any I input(s)? If it exists, Does it based on each U or pattern of U? If it does, give me some example(s)? If it does, explain the algorithm?
  • Since all possible computations can be done with TM, Is there an algorithm to make TM simulate any algorithm P written in any language? If it exists, give me some example(s)?
  • If both questions above exist the algorithm, Why don’t we just make a single UTM U and use it to program itself then do every possible computation?