When discussing something that happened, or happens, during a period of time, is very difficult to give a set of rules regarding when to use 'over' or when to use 'during'. Sometimes you must use one of them, other times you must use the other, and at other times again you can use either one of them.
As a very general rule, 'over' is generally preferred when you are talking about something that happens regularly or continuously during a period of time, although during cannot always be excluded. On the other hand, 'during' is more likely to be used if you are speaking about something that:
(a) only happened once, or perhaps a few times, during a time period, e.g. I went to the movies three times during the holidays, or
(b) something that happened at some time during a longer period of time, e.g. The Grand Final will be held during August, or
(c) something that happened at some unknown time during a larger time period, e.g. We believe the theft occurred at some time during the weekend, or
(d) something that happens during a named time period, e.g. 'during the war', 'during the depression', 'during the '40s', 'during the Elizabethan period', 'during the Clinton administration'.
However,it is also possible to use 'over' for both (a) and (c) above, but less likely for (b).
With respect to each of your sentences, I will place a + sign if I think it is acceptable, a - sign if I think it is not as acceptable, and an * if I think one answer should be preferred over the other.
Will you be home over the summer vacation? +
Use this if you mean 'Will you be home for most or all of the summer'.
Will you be home during the summer vacation? +
Use this if you mean 'Will you be home at any time during the summer'.
Over a period of ten years he stole a million pounds from the company.
+
Use this if you mean money was stolen regularly throughout the ten year period, totaling a million pounds. i.e many small thefts
During a period of ten years he stole a million pounds from the
company. +
Use this if you mean that at some stage during the ten year period he stole a million pounds. i.e. a single theft, or possible a few large thefts.
Wages have fallen by more than twenty percent over the past two
months. +*
Wages have fallen by more than twenty percent during the past two
months. +
Either is possible, but I prefer 'over the past two months'. Generally, this sentence would make more sense with a longer time period (eg six months).
Plants need to be looked after and protected over bad weather. -
Plants need to be looked after and protected during bad weather. +*
I can't say why, but 'protected during a time period' sounds much better to me than 'protected over a time period'.
American business in Britain over the 1950s grew much faster than
British business. -
American business in Britain during the 1950s grew much faster than
British business. +*
'The 1950s' is a named time period.
Over his lifetime he was relatively unknown. -
During his lifetime he was relatively unknown. +*
'During his/her lifetime' is the commonly accepted form, although 'over his lifetime' is not entirely unknown.
Many strikes over the last few years have not ended successfully. -
Many strikes during the last few years have not ended successfully. +*
Strikes tend to occur sporadically over a period of years, rather than continuously, so I prefer 'during'.
Best Answer
This sentence sounds fine to me. I do not think it should be "over the two days" or "during the two days", because that expression would suggest that the event spanned both days. Do you think the writer was out at sea on a boat for 48 hours constantly? It doesn't read that way. It says that they "went" on two days, which suggests that they took two trips out on the boat, one on each day. If you take a trip that lasts for two days, you only "go" once. It is quite correct then to say that they were unlucky "on the two days", because they had the same experience on each of those days.