Is an infinite tape alphabet for TM valid? Can I use an infinite alphabet for the tape in a turing machine? 

e.g. with input string as (1, 0)* 
can I define the symbol 1j as the symbol 1 with j marks on top of it where j in a natural number, to be used on the tape?
Turing machines have a finite tape alphabet.

You can think of a generalization of Turing machines with infinite tape alphabet, but there are two problems:


The description of the machine is no longer finite.
Such a machine can decide any language over $\{0,1\}$ (exercise).


There are ways around it - for example, we might require the rules to be finitely specifiable in some specific form. The resulting model will then be equivalent to Turing machines (in terms of computability).