Near our office building, there is street parking, but for. To savinge money we usually park on the non-parking roadside although it's hard to find a spot.

You can check out some Independent and Dependent clause lessons online for better sentence grammar.

Yesterday day I couldn't be bothered to find a spot, so I parked my car on the parking roadside.

When I was walking during my noon break time, I found all the cars(nearly 50) parked on the non-parking roadside were tickfined and the owners had to pay for a ￥200 fine.

Noon break time not a word in English. Usually say lunch break or just break at noon.
Since it is time, saying during instead.
Ticked not the correct word here. Usually say fined (getting a ticket).

I felt I was so lucky I didn't park there today.

On the other aspecthand, I don't understand why the issuers always catch us off guard when giving out parking tickets and how they ticket so quickly.

On the other aspect not a transition word. Use on the otherhand instead.
I’m not sure what you meant in the last sentence. Are you saying that I’m not sure why the officers give out tickets quickly and randomly (out of nowhere)?

Near our office building, there is street parking, but forto savinge money, we usually park on the no-parking roadside although it's hard to find a spot.

Yesterday day I couldn't be bothered to find a spot, so I parked my car on the parking roadside.

When I was waltaking a walk during my noonlunch break time, I found all the cars (nearly 50) parked on the no-parking roadside were ticked and the owners had to pay for ￥200 fine.

Near our office building, there is street parkThere is street parking near our office building, but forto savinge money we usually park oin the no-parking roadsidezone, although it's hard to find a spot there.

"Zone" means "area" and "no-parking zone" is a common phrase.

Yesterday day I couldn't be bothered to findlook for a spot there, so I parked my car on the parking roadside where parking is allowed.

When I was walking during my noon break time, I found that all the cars (nearly 50) that parked oin the no-parking roadsidzone were ticked, and the owners had to pay fora ￥200 fine.

I felt I was so lucky I didn't park there tohat day.

On the other aspecthand, I don't understand why the issuerparking enforcement always catches us off guard when giving out parking tickets, and how they write tickets so quickly.

"The issuer" is a vague phrase to use for this situation. "Parking enforcement" or "the police" makes more sense.