Hello. I need some grammar and lexical help.

Question

1)Is it possible to use the infinitive with "purpose/goal/objective/aim": "the initiative has a purpose/goal to improve the situation"
2)is it possible to say "the visit intends to demonstrate..." (or is "intend" used about people?)
3)is it possible to say "questionable/questioned territory" about disputed territories
4)which is correct,will or would, in the sentence: they belive the countries will/would hardly sign an agreement.
5)are "remain" and "stay" synonyms in the phrase "they remain / stay unshakeable in their position"
6)is it natural to say: "the remarks started criticism"

And one more question please: are such words as "however, nevertheless, though" separated by commas or does it depend on their position in the sentence?
Thank you very, very much for all your help.

Answer 1

#1 would be better phrased like this:
The purpose of the initiative is to improve ...

#2 - intend is used for people, yes. You could write this: The purpose of the visit is to demonstrate ...

#3 - It would be better to refer to questionable boundaries or boundaries in dispute.

#4 - Read these:
http://grammar.ccc.commnet.edu/grammar/verbs.htm#sequence
and
http://grammar.ccc.commnet.edu/grammar/sequence.htm
Since you have a simple present (believe) for your main verb, what should you have following it?

#5 - Yes, they are synonyms for each other.

#6 - I don't know how remarks can start anything. To me, "start" is more of a human activity. You could say, "The remarks resulted in criticism..."

However, nevertheless, though -- it depends on how they are used. Most of the time (but not always), they should be used in a compound sentence with a semicolon before them and a comma after. They are called conjunctive adverbs (and "though" can also be a subordinating conjunction):
http://grammar.ccc.commnet.edu/grammar/transitions.htm#transitions
Scroll down to the chart. If you give me your whole sentence I can help you better with these.