(I'm learning a contracted formions. If there's are any words that can be contracted, please correct ithem.) There' are some cafes I usego to to study English after work. (I'm learning contractions. If there are any words that can be contracted, please correct them.) There are some cafes I go to to study English after work.

Typically, you only contract "are" with pronouns, such as "you're" or "we're." I would never contract "there" and "are" when writing.

(I'm learning a contracted formions. If there's are any words that can be contracted, please correct it.)that I have missed, please do so.) There're some cafes I use to study English after work. (I'm learning contractions. If there are any words that can be contracted, that I have missed, please do so.) There're some cafes I use to study English after work.

Yesterday, I found the cafe I like the mostat my favorite cafe was closed. Yesterday, I found that my favorite cafe was closed.

This sounds more natural.

Yesterday, I found out that the cafe I like the most was closed. Yesterday, I found out that the cafe I like the most was closed.

To me, this cafe's a place with something like spiritual energy, so I felt like my TOIEC score got higher and higher as I studied at this cafe. To me, this cafe's a place with something like spiritual energy, so I felt like my TOIEC score got higher and higher as I studied at this cafe.

To me, this cafe' is a place with something like a spiritual energy,so: my TOIEC score got higher and higher as I studied at this cafthere. To me, this cafe is a place with something like a spiritual energy: my TOIEC score got higher and higher as I studied there.

In this case, not using a contraction would sound better.

I went to another cafe, which I like the second best, but it was also closed. I went to another cafe, which I like second best, but it was also closed.

I went to another second cafe that I like the second, but it was also closed. I went to a second cafe that I liked, but it was also closed.

That cafe's bread was cheap, but tasty. That cafe's bread was cheap, but tasty.

That cafe's bread wae bread from that cafe is cheap but tasty. The bread from that cafe is cheap but tasty.

In this case, not using a contraction would sound better.

Reluctantly, I went to a cafe chain reluctantly. Reluctantly, I went to a cafe chain.

Your sentence is not wrong, but this sounds more natural.

So I went to a cafe chainhain-cafe reluctantly. So I went to a chain-cafe reluctantly.

Minor style point.

CThe coffee and sandwiches' there are not good, but also not cheap; t. The couple ton the right of me started to have a quarrel; tfight. The two young girls behind me were speaking ill ofbadly about someone; a. A man and a woman on the front-left were also bad-mouthing someone, so I felt helpless. The coffee and sandwiches there are not good, but also not cheap. The couple to the right of me started to fight. The two young girls behind me were speaking badly about someone. A man and a woman on the front-left were also bad-mouthing someone, so I felt helpless.

My changes sound a bit more natural. Things like "quarrel" or "speaking ill" might be considered old-fashioned.

CThe coffee and sandwiches' are not good but notor cheap; t. The couple on the right of me started to have a quarrel; t. The two young girls behind me were speaking ill of someone; a. A man and a woman on the front-left were also bad-mouthing someone, s. So I felt helpless. The coffee and sandwiches are not good or cheap. The couple on the right of me started to have a quarrel. The two young girls behind me were speaking ill of someone. A man and a woman on the front-left were also bad-mouthing someone. So I felt helpless.

The limiI ran out of my patience to stayafter being there wasfor 15 minutes. I ran out of patience after being there for 15 minutes.

The limit of my patience toI could only stay there was 15 minutes. I could only stay there 15 minutes.

This version is more to the point.