Watching sports programs is a good use of time, because after a busy day people need to relax, and watching sports programs is a good outlet.(1) Relax does not require the reflexive. (2) In standard usage, sentences shouldn't begin with and (although many writers do this for reasons of style), so you should connect these two sentences with a comma. (3) Because you have several commas, I would delete one to help the sentence flow better. Comma placement in English is sometimes flexible, and this is one of those cases!
Personally, I like to watch soccer games... I get excited when Messi scores a goal.For me, Iwouldlike to watch soccer games, especially Spanish League. I am excited when Messi scores his goal.(1) "For me" is not bad, but it sounds a little juvenile to my ears. (2) The simple present like is better because it indicates that this is something true about you, or a regular habit. Would like is for requests or conditions, such as, I would like tea with my dinner, please. Or I would like to watch a soccer game if there's one on TV tonight. (3) Again, simple present am should be used with personal truths or characteristics; get (or become) shows that Messi is causing you to become excited. (4) "His" is okay, but the goal really belongs to the team, doesn't it?
Watching ... encourages me spiritually. For example, before Liuxiang became a famous athlete in my country, he had to...What’s more, watching sports programs encourages me spiritedly. Let’s say, Liuxiang, a famous athlete in my country, before he became famous, he had to practice 10 hours every day. Due to his efforts, he became the 110m hurdles world champion.(1) Spiritedly means "with spirit", as in, The band marched spiritedly to the sound of their music. Spiritually means "with relation to to the spirit or soul". (2) The second sentence just needed to be simplified.

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