What is the difference between halting, accepting, and deciding in the context of Turing machines?

Question

Does accepting mean that the TM will read and recognize a char from the cell it's currently reading from? And is it the case that a TM halts iff the input is decidable?

Answer 1

Every Turing Machine M defines a language L(M). This Turing machine M can recognize that language L(M).

Give an input, a TM has three outcomes when running/working on that input: (1) halt and accept, (2) halt and reject, and (3) reject by looping.

A TM decides a language means this TM halts on every input: it either halts and accepts if that input belongs to L(M), or halts and rejects if that input does not belong to L(M). Notice it never rejects by looping if it decides a language.

Given a language, if you can design a TM to recognize (decide) that language, we say that language is recognizable (decidable).

"the input is decidable" does not make sense to me. You can accept or reject an input. You may be able to decide a language, and some languages are not decidable (for example the halting problem). We don't say we can decide an input.