The Four Seasons in Japan : Spring 日本の四季　：　春

Spring in Japan comes gradually from the south region. (Your sentence is ok but is a little unnatural. - You could say "Spring starts earliest in the south of Japan and then spreads gradually to the rest of the country.")
日本の春は南の方から徐々にやってくる。

In these days, all TV stations report "a cherry blossoming forecast" along with with a the weather forecast all together.
この頃になると、すべてのテレビ局は一斉に”桜の開花予報”を天気予報と一緒に放送する。

This is because all the Japanese people are looking forward to seeing the cherry blossoms in full bloom.
日本人が皆、満開の桜をたのしみにしているからだ。

Spring, as well as the with cherry blossoms, is going spreads up from the south region of Japan to the middle region part of the country (including Tokyo) and then Hokkaido in the north of region through Japan. (We don't usually need to put a space after and before brackets.)
日本の南から関東、北海道へと春は桜の花とともに日本を縦断していきます。

The days of the full bloom of that cherry blossoms are in full bloom are about five days or so, at most.
桜が満開に咲いているのは長くてせいぜい五日。

During these days, we enjoy cherry-blossom-viewing-parties, having feasts and beyond without doubt some people may will sing Karaoke songs. (beyond doubt/without doubt - means "certainly", so you should use "will" instead of "may" as, "may" means "not certainly".)
この間に、私たちは宴会を、人によってはカラオケも、たのしみます。

Spring runs through the land of Japan by spending time for in just over one month.春は一ヶ月以上かけて日本を縦断していく

Hope the corrections are helpful. Great writing!