i would give it a tick behind if i was the one who said so, that doesnt mean it's not correct the other sentences, but according to those examples from your book, i could finally tell why those chinese language learner speak in such a strange way, which makes people notice immediately that it's a foreigner speaking, the book you are using is not good. Seriously, i think the way you say is way more better(i mean the sentences you've given after those examples)
1.After I graduate I will go to China to teach English
我毕了业以后到中国去教英语。
我毕业了以后去中国教英语。√
我毕业了以后到中国教英语。
2.I went to China again last year
我去年又到中国去了。
我去年又去了中国。√
我去年又去中国了。√
3.I am going to China again next year:
我明年会再到中国去。
我明年会再去中国。√
Can I say it without the 会?
我明年再去中国 : it implies the following information: i have another plan for THIS year, so i will visit China the Next year. saying so, you change the meaning of '再' , no more signify 'again' in this case.
我明年会再去中国: it implies the following information: i have already been to China, the next year i will pay another visit to China again.
no gramatical problem in these two sentences, but two meanings. from this sentence, i notice how difficult chinese is - -# cheer up..