This time, I do not have to worry travelling so far away anymore.


The sentence seems OK without the underlined portion.

This time, I do not have to worry travelling so far because it will take place in Frankfurt on the 8th of March2015.

Right?

Kodachen1This time, (no comma) I do not have to worry about travelling so far (away) (anymore).

As shown. It's "worry about (something)".

CJ

Kodachen1This time, I do not have to worry travelling so far because it will take place in Frankfurt on the 8th of March2015.

Presumably your reader knows what "it" is. You need this:

This time I do not have to worry about travelling so far because it will take place in Fr

........so far because it will take place in Frankfurt on the 8th of March2015.

is the red underlined, right?

This time and anymore do not belong together in the same sentence.

I do not have to worry about travelling so far away anymore. (This time and all through the future.)

Kodachen1........so far because it will take place in Frankfurt on the 8th of March2015.is the red underlined, right?

No. This has been answered above. ... 8th of March, 2015.

CJ

For an annual event:

This time I do not have to worry about travelling so far because it will take place in a city very close to me, Frankfurt.
Next year I will have to worry about travelling a long distance because it will take place in Sidney, Australia.

--------------------------
I do not have to worry about travelling so far away anymore because it will always

8th of March, 2015.

With comma?

Kodachen18th of March, 2015.With comma?

I would definitely use a comma there. Yes.

CJ