It is definitely a complex issue and you raise some good points.
On your specific cases:
1. International students - maybe I'm missing the point, but don't international students generally go home once they graduate? In which case if the overall population of intl student is steady, they shouldn't materially affect the numbers.
2. Workers in specific sectors - while I am generally in favour of people coming here who have skillsets that allow them to be net contributors, I said above that where certain sectors have demonstrable shortages that require relatively lower skilled immigration that that is OK in principle (but clearly needs to have some mechanisms to prevent abuse of the rules).
I stand by my point above that increasing the net population of the UK by an amount more than a city the size of Manchester every year into the indefinite future isn't sustainable.
The old 'taking our jobs' and 'draining our services' have become weaponised to some degree, but in the end it is generally the UK working class who suffer from increased competition from lower skilled labour from abroad so it is an issue for many. And where there is a finite supply of services (for example doctors appointment or school places) then those coming to the UK are putting added strain on those services. That said, I would have thought that housing is the biggest issue as they all need somewhere to live and the current rate of immigration exceed even Labour's stated house building targets, never mind what it will actually achieve on that front.
