When should a person file a PCT? How can I find out which countries a PCT covers? How much does it cost?
When to file
There are many possible answers here.
If what you are seeking to patent is already made public (in a brochure, a scientific paper, a presentation) then it is probably too late. A skilled attorney may get you out of this, depending on the situation, but there will be no guarantee.
If you have already filed a national patent application (e.g. in Denmark or the US) then you have strictly 12 months to file a PCT application and claim priority.
If you have done nothing of the above, you can file a PCT application as soon as you wish. That of course means you have some work to support your patent. Better have a professional to write down the patent, as it is not as easy as it might look.
The current list of countries and regions under the PCT can be found here http://www.wipo.int/pct/en/pct_contracting_states.html
As for the cost, this is really hard to answer. First of all there is the cost for filling a PCT and paying for the search report and relevant formalities, a little over 3000 euros. A quick view can be found here https://www.epo.org/applying/forms-fees/international-fees/important-fees.html
After filling the PCT, you will have to decide which countries you want to have your patent granted. For each country (or region, like the EPO) there is the cost for the patent prosecution (patent attorney cost and patent office actions) and then there is the cost for maintaining a granted patent.
Obviously there is no straightforward answer here, but for major markets expect 4-digit numbers for the first examination steps (and see again wikipedia https://en.wikipedia.org/wiki/Patent#Economics the paragraph for costs)