Matching fully balanced with unbalanced.

.i just try to understand if it beneficial to go balanced as far as I can in the system chain if I have unbalanced amp at the end anyway.

The answer to this bit is 'yes.'

BTW, that opamp chops a full audio sign-wave into a negative and a positive,

Huh?? No it doesn't. An opamp has two inputs, inverted and non-inverted, and otherwise is a DC coupled amp with very high gain. for audio purposes, to control the gain and allow the opamp to operate in a linear fashion (otherwise the output tends to spend a lot of time at one rail or the other), feedback is applied. The resulting gain is thus then the ratio between the input resistor in series with the inverting input and the value of the feedback resistor. It does not chop the signal or anything like that- the output is single-ended, and in phase with the '+' input and out of phase with the '-' input.

Sure. But its likely that the amp, even though equipped with an XLR connection, isn't actually processing the signal fully. If the equipment supports the balanced standard (and in high end audio most of it does not) you will run into a buzz problem, although that is easily solved. If the equipment doesn't support the balanced standard, you likely **won't** encounter buzz. I know this sounds counter-intuitive, but that's how it is.