In China, we ues "南边“ more than “南部”. And when you can use “南部”,you can use "南边“,too in most cases. ( Also, we Chinese do not care the fifferences between 南部 and 南边 much.)Therefore,
1. for this problem:
(Is it correct that for example I have to say:
香港在广东省的南边. (Because Hong Kong is not part of Guangdong)
And:
广州在广东省的南部 (Because Guangzhou is part of Guangdong) )
I think thses two sentences "香港在广东省的南边. " and "广州在广东省的南部"are right
,and your reasons are correct.
2. for this problem:
(So the following sentences are wrong?
香港在广东省的南部.
香港在广东省的南边.)
My answer is that they are not right completly and just look these sentences.
香港在广东省的南部.(wrong)
香港在广东省的南边.(right)
广州在广东省的南部.(right)
广州在广东省的南边.(right)
3, for this problem:
(Or can I just use 南边 and 南部 interchangeably?)
I want to say you can do it in most cases because we do not care the differences of the two words tmuch.( To be strict, the two words cannot be interchanged.)
4, for thim problem
(补充说明:
Also, is there a difference between 南边 and 南面?)
My answer is yes.
Similarly, in most cases,they can be interchanged but there are exceptions,for example,
这面墙的南面有张画。
这面墙的南边有张画。
The two sentences have the differently.
--------Hope I can help you. You can ask me when you have any problem if it is convenient for you.