Введение -- Titles are always capitalised. The fine thing: if you mean here introduce yourself, it's more appropriate to say "O себе"; "Введение" sounds like you start a book or academic paper.

Здравствуйте, меня зовут Michael (Майкл). -- Here you greet and then introduce yourself. These are two different "minor sentences" within a "major" one. Therefore the greeting "Здравствуйте" in the beginning of this sentence is divided from the rest part with a comma.

Я люблю путешествия, подводное плавание, пеший туризм и лыжный спорт например хобби. -- Regarding the comma before "и", it was explained by previous "spell-checkers", so I'll focus on the other things. First of all, I must say that this is a pretty ambiguous sentence in its initial form. Ambiguity is because of using "я люблю" and "хобби" in one phrase. In Russian we call it "масло масляное", i.e., when you repeat differently sounding words having nearly the same sense in fact (show me the one who doesn't like one's hobby - because hobby is a priori something that one enjoys to do!). And the most ambiguous is that "например".

I've read your addition in comments, so can derive a pretty good version of this sentence with explanation. The final phrase, IMHO, sounds better when split into two. "Мне нравится путешествовать. Другие мои хобби это, например, подводное плавание, пеший туризм и катание на лыжах". -- (1) In Russian, we cannot say that we like TRAVELLING (English gerunds that carry sense of verb+noun have no analogs in Russian). We also almost don't use nouns to express this sense, however, if you'll say so, people will understand. But the most common way to express this is to use verb like I did above. It's absolutely the same if you'll say "I like to travel". (2) Here I placed the word "хобби" in the beginning and specified these are "[your] other hobbies". The word "например" is always separated by commas on both sides. The rest of your hobbies can be pronounced as nouns in Russian. The only thing I changed is "лыжный спорт" to "катание на лыжах", because it seems you do not make it professionally. But if you're really a pro at it, then the end of this sentence should be a bit different...

1.Your mistakes here are the same you'll have with the literal translation.

I.e.: "я люблю путешествие" = 'I like [a/the] travel".
"Я люблю путешествовать" = "I like to travel".
"Я люблю путешествия" = "I like travels", but the Russian version sounds better here.

2.you don't need ',' before 'и' here - just like in British.

3."например хобби" sounds exactly like "...for example hobby". I cann't guess what did you mean here:/

4. "Пеший туризм" and expecially "лыжный спорт" are formal names. In the latter case one may think that you just like to watch winter Olympics. Didn't you mean that?

There exist more informal ways to express it. And "лыжный спорт" is ambiguous: many Russians practice cross-country 'nordic' skiing (i love iot myself), while downhill 'alpine' skiing is preferred in hotter counries. "Лыжи", "кататься на лыжах" by default assume the former activity.
To evade ambiguity in the latter case we specify: "горные лыжи", "сноуборд", "горнолыжный" (...спорт, ...курорт, ...трасса) etc.

введение

здравствуйте меня зовут Michael (Майкл).
Я люблю путешествиеовать (it sounds more natural, but you also you can say "путешествия"), подводное плавание, пеший туризм, и а, лыжный спорт - это мое хобби.


P.S if possible could you please explain in English the mistakes reasons
спасибо

Введение.

Здравствуйте! Меня зовут Michael (Майкл).
Я люблю путешествие, подводное плавание, пеший туризм, и лыжный спорт например хобби.


P.S if possible could you please explain in English the mistakes reasons
спасибо

Введение

Здравствуйте! Меня зовут Michael (Майкл).
Я люблю путешествовать, заниматься подводным плаванием, увлекаюсь пешим туризмом, а также лыжным спортом.


P.S if possible could you please explain in English the mistakes reasons
спасибо