我是大學生，也今年畢業的大學生。

It would be more natural to say it with just one sentence. If you want to split it into 2, you could say "我是大學生，我今年會畢業／我今年畢業了。" :)

我的愛好是玩視頻電子遊戲和語言學習語言。

"視頻" does mean "video" but you usually use it as a standalone noun, like "我在看一段視頻" which means "I'm watching a video."
You could also pair it with other nouns when you want to specify the type/purpose of the video. For example, "我在看一段關於中文的教學視頻。" which means "I'm watching a video that teaches Chinese." (sorry my translation sounds a bit weird but I think you get the gist hahahx)
For video games, you'd say "電子遊戲" :)
And "語言學習" makes perfect sense but it'd be more natural to say "學習語言", just like you did with "玩電子遊戲" when you put the verb first :)

我學了中文兩個月。／我學中文已經兩個月。

You'd need to add "了" after the verb if you want to express that you've been doing this action for quite some time (i.e. present perfect tense)

我也在學日文。

In Chinese, It would sound more natural to say "I'm also studying Japanese." instead of "I also study Japanese", which makes perfect sense in English. Just so you know! :)

我是大學生，也今年畢業的大學生。

one sentence will be more perfect!

我學中文已经兩個月。

show duration

我是挪威人。，

我也是大學生，也今年畢業。

我的愛好是玩視頻電子遊戲和語言學習語言。

我學中文兩個月。已經學了兩個月的中文，

我也同時也在學日文。