Civil marriage abroad and implications for children

Hello Rabbi,
I will describe a case and ask what the halachic implications are:
data:

• A single Jewish woman married a Jewish man in a foreign country for the purpose of obtaining citizenship of that country (the man is a citizen of that country and the woman is not).
• The marriage ceremony was held in a purely civil format, as is customary in that country. For that matter, there was no rabbi, seven blessings, etc.
• The couple was not religious (there may have been an affinity for tradition and faith in God, but by and large they did not observe Torah and commandments).
• The couple does not actually live together and does not have marital relations.
• After a period of time, the woman received citizenship and the couple divorced civilly.

Questions:

1. Does this marriage qualify for halachic kiddushin? Is the woman considered a man’s wife even after the separation, (or was she not considered his wife from the beginning?) and does a divorce according to halachic law require it?
2. Will children born to the same woman by another man later in her life be considered bastards? Does it matter whether she married the “new” man or not?
3. Do the answers to 1 and 2 depend on each country’s specific laws regarding civil marriage (e.g., the type of contract signed, is there a separation of religion and state, etc.)?
4. Do the answers depend on whether the civil legal level of the separation process was a civil divorce or an annulment of marriage under the laws of that country?
5. Do the answers depend on the man receiving a sum of money for this wedding for the purpose of citizenship?
6. If the man is same-sex, could this affect the answer (for example, perhaps it could be assumed that in any case he did not intend to sanctify her in order to live with her as a halakhically married couple)?
7. Can the existence of some of the conditions together in 3-6 affect the answer, in the case where the existence of each one alone does not change the answer?

Thank you very much (and in general for the site).