Anime: Gekkan Shoujo Nozaki-kun [6]

チャリ通（ちゃりつう）it means to go (to a place) by bicycle
乗っける（のっける）this is casual form of 乗せる; it means to give someone a ride

荷台（にだい）for bicycle, this is the luggage carrier at the back. Sakura was saying Nozaki's bicycle might not have it. It's quite freaky the solution is to stand on the frame though... what if you touch the wheel? ^^;

４輪チャリ（よんりんちゃり）4-wheeled bicycle
二人乗り（ふたりのり）two people on the same vehicle

レジャー（れじゃー）leisure
信頼感（しんらいかん）trust

In this scene, Nozaki said 「そうか…後ろが漕いじゃいけないんじゃないか？」

漕ぐ（こぐ）means 'to pedal'.

How did it become 漕い in the sentence? The te-form of 漕ぐ is 漕いで, and じゃ is slang for では, so I think it was originally 漕いでは (te-form + は topic marker).

Besides the common では→じゃ, there are also ければ→きゃ, ては→ちゃ. There may be more but those are what I can recall in my mind.

In this scene, Sakura said 「自分だけ何もしてない罪悪感ハンパないよ‼︎」

罪悪感（ざいあくかん）feelings of guilt
ハンパ（はんぱ）this means things like fraction, incomplete, not full etc. If I remember correctly, if you put the word はんぱ to an action, it means that it's not done wholeheartedly. If you watch anime enough you might have come across this word. It's often said to a character who is hesitating.

In the sentence, it's ハンパない, so it's the reverse meaning. If I were to translate 罪悪感ハンパない literally to English, it would probably be 'the feelings of guilt are not mere/minor/small/light!!'

In this scene, Nozaki asked Sakura to 腰に手を回す（こしにてをまわす）which means to put her arms around his hip. His back is too far for her though and hence the result ^^;