Do 기 and 는 것 have the same functions?
1.The function of 기 is changing verb into noun, isn't it?
So, if I want to say my hobbies are swimming and cooking=
내 취미는 수영하기는 하고 요리하기는이야, is it right?
2.If 내 취미는 수영하는 것 하고 요리하는 것이에요, is it also right?
If I also can use 는 것, it means that this pattern also can change the verb into noun, doesn't it?
3.In this sentence, 내 어머님은 맛있는 음식을 요리하는 것이라고 생각한다,
는 것 form in this sentence also changing verb into noun like number 2 above?
4.In Korean grammar for adjective, verb, and noun always follow this rule?
ㄴ/은 ~ = for past/과거
는 ~ = for present/현재
ㄹ/을 ~ = for future/미래
For example even that past future-would also use ㄹ/을 ~ form?
Thank you for the answers.

Question

Do 기 and 는 것 have the same functions?
1.The function of 기 is changing verb into noun, isn't it?
So, if I want to say my hobbies are swimming and cooking=
내 취미는 수영하기는 하고 요리하기는이야, is it right?
2.If 내 취미는 수영하는 것 하고 요리하는 것이에요, is it also right?
If I also can use 는 것, it means that this pattern also can change the verb into noun, doesn't it?
3.In this sentence, 내 어머님은 맛있는 음식을 요리하는 것이라고 생각한다,
는 것 form in this sentence also changing verb into noun like number 2 above?
4.In Korean grammar for adjective, verb, and noun always follow this rule?
ㄴ/은 ~ = for past/과거
는 ~     = for present/현재
ㄹ/을 ~ = for future/미래
For example even that past future-would also use ㄹ/을 ~ form?
Thank you for the answers.

Answer

I think you've found one of secrets of our language.:) 
yes, you are totally correct, 
but somehow the sentences you put as examples are inappropriate, I guess. 

1) the first sentence should be 
"내 취미는 수영하고 요리야". 
in here, I don't feel it's necessary to put "~기" to make the verbs nouns because "수영하기" definitely acts like a noun but in your sentence, it's not natural. 

2) yes, the second sentence is correct, and the answer is "yes". 
"수영하는것" acts like a noun. 

3) yes, your sentence is a bit weird though. 

4) yes.:) but as you know, 
languages are not like math, there is no such an "always". 
so that, I can't say they always follow the rules, it depends. 
luckily, most things you mentioned above are correct.:)