1. I will be 17 years old next year.

2. I would be 17 years old next year.

(Is #2 corect? When can we use 'would'?)

3. The river runs south.
4. The river flows south.
(Are both OK?)

5. We have dinner when she arrives.
6. We will have dinner when she
arrives.
(Which one is right? Are both grammatical?)

7. He has been chatting with a foreigner in a chatroom for an hour.

8. He has chat with a foreigner in a chatroom for an hour.

(Are both grammatical? What is the difference between 7 and 8?)

6 answers

for your first question, we use would as a past tense.
1. I will be 17 years old next year.
2. I would be 17 years old next year.
(Is #2 corect? When can we use 'would'?)
#1 is most often used; you'd be referring to your age on your NEXT birthday. #2 is not commonly used.

3. The river runs south.
4. The river flows south.
(Are both OK?)
Yes, bot are OK; #3 is more common.

5. We have dinner when she arrives.
6. We will have dinner when she
arrives.
(Which one is right? Are both grammatical?)
Both are grammatical, but #5 is the one to use most often since you are referring to a future event.

7. He has been chatting with a foreigner in a chatroom for an hour.
8. He has chat with a foreigner in a chatroom for an hour.
(Are both grammatical? What is the difference between 7 and 8?)
#7 is perfect. #8 is not correct unless you use "chatted" for the main verb (past tense).
Sorry -- "both" not "bot" for #3!!

#6 is the one to use, not #5.
7. He has been chatting with a foreigner in a chatroom for an hour.

8. He has chatted with a foreigner in a chatroom for an hour.

(Thank you. What is the difference between the two?)
#7 means he started chatting a while ago and is still chatting.

#8 implies that he chatted with the foreigner for an hour, but has now stopped. However, this and #7 could mean the same thing!
As for "would" it is Conditional and usually implies an "if" clause. I would do that IF I could.

Actually, I'd use #6 and not #5 = we will or we'll for Future tense.

Sra