A gGood news! Good news!

(1) "News" is an uncountable noun, so we do not use "a" in front of it. The countable form is "a piece of good news". (2) You can choose to capitalise the title: "Good News!" However, I don't think it's necessary here, because "Good news!" sounds more like a complete sentence that's part of the actual writing, rather than a title.

A gGood nNews! Good News!

I'd probably capitalize these.

A gGood nNews! Good News!

If the title consists of only a few words, we usually capitalise everything.

A collaboration cafe bybetween Hazbin Hotel and Animate Cafe will be held! A collaboration between Hazbin Hotel and Animate Cafe will be held!

If you are talking about a collaboration, it is helpful for the reading to mention who the two people/companies are, that are collaborating :)

A Hazbin Hotel collaboration cafe by Hazbin Hotel will be heldopening! A Hazbin Hotel collaboration cafe will be opening!

(1) "By Hazbin Hotel" makes it sound like Hazbin Hotel owns the cafe. You can say "Hazbin Hotel collaboration cafe" instead. In this context, "Hazbin Hotel" functions more like an adjective. (2) オープンする: to open. We don't use "hold" with "cafe".

I’m so happy because I love this animeated television series. I’m so happy because I love this animated television series.

To my understanding, in Japanese, "アニメ" can refer to any animated film. Outside Japan, however, "anime" generally refers to a specific kind of Japanese animation. Hazbin Hotel is what we would call an animated television series.

The menus will change in the first and second halvesf, so I will go twice with my friends. The menus will change in the first and second half, so I will go twice with my friends.

Sentence is ok - might be helpful to expand on what the 'half' is. Half a day? Half a month? Half of the event? That makes it clearer to understand!

The menus will change ibetween the first and second halves of the event, so I will go twice with my friends. The menu will change between the first and second halves of the event, so I will go twice with my friends.

(1) "Menus" doesn't have to be in the plural form, because one cafe will have only one menu. In my opinion, the singular would sound a little more natural. (2) Using "in" implies that the menu changes twice, once in the first half and once again in the second, which means there will be three different menus. I assume this is not what you meant. (3) It's good to specify what you mean by "first and second halves".