Hi everyone!

I have panel data of the form:
Country Continent Year agprod drought
ABW LAC 1972 13413513 0
ABW LAC 1973 15213523 1
ABW LAC 1974 13513513 1
ADO WEOFF 1972 353413 0
ADO WEOFF 1973 234233 0
I am trying to pinpoint the effects of drought on agricultural production and have a model of the form:
Array
I am fine with the country FEs and the year FEs which I use to account for omitted variable bias. As such, I eliminate bias from time-varying unobservables that are constant across countries as well as eliminate bias due to factors that differ across countries but are constant over time (?).

Now, my issues:

1) I have been advised to include continent*year FEs instead of simple year FEs and I am struggling with the intuition behind this. I understand that I am in effect disaggregating the effects of year into separate year dummies for each continent and thus assuming that the time-varying unobvservables vary differently according to different continents... But I still am shaky about my understanding, if someone could clarify this and maybe have a pertinent example of the effects that are controlled for.

I've included these continent*year effects using reghdfe ln_agprod drought, absorb(country continent#year). Is that correct?

2) I would like to take into account time trends to see if I get different results. I am not interested in the coefficients for the trends but this would only be used to see the impact on the coefficient of drought. First of all, I assume I cannot include time fixed effects if I am including a time trend in my model (?). What is the difference between having time fixed effects and a time trend? I assume the trend incorporates the year effects?
I was advised to include country-specific time trends. So in my mind, I would include these country-specific time trends as well as country FEs but not year FEs.
Any idea of how I can do so in Stata? Would reghdfe ln_agprod drought, absorb(i.country##c.year) do the trick? or reg agprod spei i.country##c.year ?

Also has a clear way to explain the intuition between a model with 1) country fixed effects and year fixed effects only, 2) country fixed effects and continent*year fixed effects, and 3) country fixed effects and country-specific time trends? I feel a bit shaky about my understanding and would like to feel confident about what variation I am taking account for in each case.

Many many thanks in advance!